Number Properties : Divisibility

This question tests  your understanding of divisibility.

Question

If K is divisible by 3, 4 and 5, which of the following will also divide K?
I. 3, 4 and 15
II. 12, 15 and 18
III. 5, 20 and 30

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only

Correct Answer : Choice D. I and III only.

Explanatory Answer

If K is divisible by 3, 4 and 5, K has to be a multiple of 3, 4 and 5.

So, K is a common multiple to 3, 4 and 5.

The least common multiple (LCM) of 3, 4 and 5  = 60

Therefore, K is either 60 or a multiple thereof.

Now, let us evaluate whether the numbers in the three choices I, II and III will divide 60.
Choice I : 3, 4 and 15. All these numbers divide 60.
Choice II : 12, 15 and 18. 12 and 15 divide 60. But 18 does not. 
Choice III : 5, 20 and 30. All 3 numbers divide 60.

So, the correct answer is Choice D. I and III.