Problems on H.C.F and L.C.M


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16. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

A. 279
B. 283
C. 308
D. 318

Correct Answer: C. 308

Answer Explanation:

Other number

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17. What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?

A. 196
B. 630
C. 1260
D. 2520

Correct Answer: C. 308

Answer Explanation:

the least number

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18. The ratio of two numbers is 3:4 and their H.C.F. is 4. Their L.C.M. is:

A. 12
B. 16
C. 24
D. 48

Correct Answer: D. 48

Answer Explanation:

Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.

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19. The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

A. 1008
B. 1015
C. 1022
D. 1032

Correct Answer: B. 1015

Answer Explanation:

Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015

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20. 252 can be expressed as a product of primes as:

A. 2 x 2 x 3 x 3 x 7
B. 2 x 2 x 2 x 3 x 7
C. 3 x 3 x 3 x 3 x 7
D. 2 x 3 x 3 x 3 x 7

Correct Answer: A. 2 x 2 x 3 x 3 x 7

Answer Explanation:

Clearly, 252 = 2 x 2 x 3 x 3 x 7.

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