If the least common multiple of 9, 10, 12,
and v is 540, which of the following
could be v? Choose the correct choice from the following options: A) 18 B) 24 C) 27 D) 36 E) 45
To begin, notice that 540 isn’t a multiple of 24, so you can rule out Choice (B). Now find   the least common multiple (LCM) of 9, 10, and 12. The LCM of 9 and 10 is 90, so the LCM of   9, 10, and 12 must be a multiple of 90. Here are the first six multiples of 90:   90, 180, 270, 360, 450, 540   The number 180 is a multiple of 12 as well, so the LCM of 9, 10, and 12 is 180. However, 180   also is a multiple of 18, 36, and 45. So if any of these numbers were v, the LCM of 9, 10, 12,   and v would be 180. As a result, you can rule out 27hoices (A), (D), and (E), leaving 27hoice(27) as your only answer.
<result>C</result>
If the least common multiple of 9, 10, 12,
and v is 540, which of the following
could be v?