🔗 SSC GD, MTS, Railway

LCM and HCF — formula, example and practice

HCF × LCM = product of two numbers. Word problems hide this identity.

Content type: original worked example. Not labelled as a previous-year question.

Timed GK/quant mock Shortcuts CBSE Class 10 Maths 150 questions

Formula

For two numbers a, b: a × b = HCF(a,b) × LCM(a,b)

HCF is the greatest common divisor. LCM is the least common multiple.

What you should learn here

Prime-factor method: HCF takes lowest powers, LCM takes highest powers.

Worked example

Question. HCF = 12, LCM = 180, one number = 36. Other number?

Solution. Other = (12×180)/36 = 60.

Common mistake. Using the product identity on three numbers without extra care (it is stated for two).

When to use the shortcut. Bells, traffic lights and “together again” word problems are LCM. “Largest tape that measures both” is HCF.

Related chapters and tests

Ages Percentage Ratio and Proportion Profit and Loss All formulas SSC GD mocks SSC CGL mocks

150 important LCM and HCF questions

Original arithmetic practice for this page. Not labelled as previous-year SSC/railway items. Tap an option to mark it. Open “Answer” for the working.

Q. 1ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 2ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 3ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 4ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 5ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 6ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 7ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 8ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 9ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 10ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 11ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 12ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 13ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 14ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 15ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 16ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 17ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 18ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 19ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 20ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 21ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 22ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 23ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 24ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 25ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 26ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 27ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 28ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 29ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 30ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 31ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 32ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 33ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 34ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 35ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 36ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 37ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 38ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 39ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 40ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 41ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 42ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 43ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 44ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 45ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 46ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 47ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 48ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 49ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 50ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 51ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 52ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 53ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 54ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 55ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 56ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 57ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 58ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 59ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 60ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 61ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 62ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 63ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 64ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 65ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 66ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 67ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 68ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 69ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 70ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 71ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 72ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 73ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 74ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 75ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 76ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 77ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 78ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 79ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 80ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 81ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 82ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 83ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 84ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 85ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 86ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 87ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 88ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 89ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 90ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 91ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 92ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 93ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 94ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 95ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 96ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 97ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 98ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 99ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 100ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 101ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 102ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 103ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 104ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 105ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 106ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 107ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 108ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 109ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 110ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 111ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 112ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 113ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 114ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 115ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 116ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 117ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 118ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 119ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 120ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 121ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 122ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 123ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 124ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 125ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 126ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 127ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 128ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 129ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 130ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 131ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 132ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 133ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 134ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 135ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 136ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 137ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 138ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 139ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 140ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

Q. 141ल.स./म.स.

LCM of 8 and 12 is

Answer / solution

Correct option: D

LCM = product/HCF = 24.

Q. 142ल.स./म.स.

HCF of 6 and 9 is

Answer / solution

Correct option: C

HCF = 3.

Q. 143ल.स./म.स.

LCM of 10 and 15 is

Answer / solution

Correct option: D

LCM = product/HCF = 30.

Q. 144ल.स./म.स.

HCF of 12 and 18 is

Answer / solution

Correct option: D

HCF = 6.

Q. 145ल.स./म.स.

LCM of 14 and 21 is

Answer / solution

Correct option: A

LCM = product/HCF = 42.

Q. 146ल.स./म.स.

HCF of 9 and 12 is

Answer / solution

Correct option: C

HCF = 3.

Q. 147ल.स./म.स.

LCM of 16 and 24 is

Answer / solution

Correct option: B

LCM = product/HCF = 48.

Q. 148ल.स./म.स.

HCF of 15 and 25 is

Answer / solution

Correct option: B

HCF = 5.

Q. 149ल.स./म.स.

LCM of 4 and 6 is

Answer / solution

Correct option: A

LCM = product/HCF = 12.

Q. 150ल.स./म.स.

HCF of 7 and 14 is

Answer / solution

Correct option: A

HCF = 7.

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