<P></P>
<P>All numbers divisible by both <IMG style="VERTICAL-ALIGN: middle" alt=4 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_13.png"> and <IMG style="VERTICAL-ALIGN: middle" alt=15 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_14.png"> are the multiples of <IMG style="VERTICAL-ALIGN: middle" alt=4 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_15.png"> and <IMG style="VERTICAL-ALIGN: middle" alt=15 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_16.png">. Since <IMG style="VERTICAL-ALIGN: middle" alt=4 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_17.png"> and <IMG style="VERTICAL-ALIGN: middle" alt=15 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_18.png"> have no prime factor in common <IMG style="VERTICAL-ALIGN: middle" class=valignBottom alt="(4 = 2^2 comma 15 = 3 times 5)" src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_19.png">, then the least common multiple of <IMG style="VERTICAL-ALIGN: middle" alt=4 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_20.png"> and <IMG style="VERTICAL-ALIGN: middle" alt=15 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_21.png"> is equal to their product, namely <IMG style="VERTICAL-ALIGN: middle" alt="4 times 15 = 60" src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_22.png">. Every other multiple of <IMG style="VERTICAL-ALIGN: middle" alt=4 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_23.png"> and <IMG style="VERTICAL-ALIGN: middle" alt=15 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_24.png"> is divisible by <IMG style="VERTICAL-ALIGN: middle" alt=60 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_25.png">. Thus, if <IMG style="VERTICAL-ALIGN: middle" alt=60 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_26.png"> is divisible by a number then all the multiples of <IMG style="VERTICAL-ALIGN: middle" alt=4 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_27.png"> and <IMG style="VERTICAL-ALIGN: middle" alt=15 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_28.png"> are divisible by that number. Therefore, it is enough to check by which number in the given options is <IMG style="VERTICAL-ALIGN: middle" alt=60 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_29.png"> divisible. Only <IMG style="VERTICAL-ALIGN: middle" alt=6 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_30.png"> divides <IMG style="VERTICAL-ALIGN: middle" alt=60 src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_31.png"> and none of the other do. The answer must be <IMG style="VERTICAL-ALIGN: middle" alt=(A) src="https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fsat.collegeboard.org%2Fmathmlgen%2Fcontent%2Fquestion%2FQOTD%2F2011%2F20110808_32.png">.</P>
<!-- -->
