Bunuel wrote:

What is the least common multiple of 18,120, 216, and 1080?

A. 1,080

B. 19,440

C. 38,680

D. 38,860

E. 38,880

To answer a question involving least common multiples it is usually helpful to look at prime factorizations.

This is a Precise approach.

18 factors into 3*3*2

120 factors into 12*10 = 2*2*3*5*2

216 factors into 2*108 = 2*3*36 = 2*3*4*9 = (2*2*2)*(3*3*3)

1080 factors into 10*108 = 10*(2*2*2)*(3*3*3)=(2*2*2*2)*(3*3*3)*5

The least common multiple involves the prime factors of all of the above.

Therefore, we need to count the largest number of 2's, 3's and 5's in the above numbers.

1080 has four 2's, 216 and 1080 have three 3's and 120, 1080 have one 5.

Therefore the least common multiple has four 2's, three 3's and one 5.

These are exactly the factors of 1080!

Therefore our answer is (A)

_________________

David

Senior tutor at examPAL

Signup for a free GMAT course

We won some awards:

Save up to $250 on examPAL packages (special for GMAT Club members)