The four members of a jazz quartet all play in different

[M7MBA]

The four members of a jazz quartet all play in different rhythms. The pianist plays in 9/8 time, meaning that his downbeats occur every 9/8 of a measure of time. Meanwhile, the saxophonist plays in 7/4 time, the harpist in 5/8 time, and the drummer in plain old 4/4 time (all with respect to the same measure of time as the pianist). If all four musicians start a song together on the same downbeat, how many measures later will all their downbeats occur simultaneously?

(A) 315
(B) 630
(C) 1,260
(D) 2,520
(E) 5,040

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

[Scott@TargetTestPrep]

The four members of a jazz quartet all play in different rhythms. The pianist plays in 9/8 time, meaning that his downbeats occur every 9/8 of a measure of time. Meanwhile, the saxophonist plays in 7/4 time, the harpist in 5/8 time, and the drummer in plain old 4/4 time (all with respect to the same measure of time as the pianist). If all four musicians start a song together on the same downbeat, how many measures later will all their downbeats occur simultaneously?

(A) 315
(B) 630
(C) 1,260
(D) 2,520
(E) 5,040

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

In this type of problems, we need to find the LCM of the numbers given. However, we see that they (except the last one) are not whole numbers. So first we can multiply each number by 8 to obtain 9, 14, 5 and 8, respectively. Next we find the LCM of these 4 whole numbers:

9 = 3^2

14 = 2 x 7

5 = 5

8 = 2^3

Therefore, the LCM is 2^3 x 3^2 x 5 x 7 = 2,520. However, since we multiplied each number by 8 earlier, as a result, we need to divide the LCM by 8 to obtain the correct answer of 2,520/8 = 315.

Answer: A