# Aptitude - Problems on H.C.F and L.C.M

### Exercise :: Problems on H.C.F and L.C.M - General Questions

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

Explanation:

 Other number = 11 x 7700 = 308. 275

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

Explanation:

``` L.C.M. of 12, 18, 21 30                 2 | 12  -  18  -  21  -  30
----------------------------
= 2 x 3 x 2 x 3 x 7 x 5 = 1260.       3 |  6  -   9  -  21  -  15
----------------------------
Required number = (1260 ÷ 2)            |  2  -   3  -   7  -   5

= 630.
```

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

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

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