Problem Solving

Hi VJesus12,

We're asked for the SMALLEST positive integer that is divisible by each of the EVEN integers between 1 and 10, inclusive. This question can be solved rather easily by TESTing THE ANSWERS. Since we're asked for the SMALLEST number, we should start with Answer A and then work our way 'up' until we find the one that matches...

Answer A: 60.... is 60 divisible by 2, 4, 6, 8 and 10.... NO, it's not divisible by 8.
Answer A: 100.... is 100 divisible by 2, 4, 6, 8 and 10.... NO, it's not divisible by 6 or 8.
Answer A: 120.... is 120 divisible by 2, 4, 6, 8 and 10.... YES, it's divisible by all the values (re: 2x60, 4x30, 6x20, 8x15, 10x12).

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote:What is the lowest positive integer that is divisible by each of the even integers between 1 and 10, inclusive?

A. 60
B. 100
C. 120
D. 160
E. 240

We need to determine the smallest number that is divisible by the following:

2, 4, 6, 8, and 10

That is, we need to find the least common multiple (LCM) of 2, 4, 6, 8, and 10:

In prime factorization form, we have:

2, 2^2, 2 x 3, 2^3, 2 x 5

So the LCM is 2^3 x 3 x 5 = 8 x 15 = 120.

Answer: C