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

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

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

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.

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

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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