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Review: Least Common Multiple
Explanation
"Every odd integer between 1 and 10" includes 1, 3, 5, 7,
and 9. To be divisible by all of these numbers, it must have as factors at
least one 5, one 7, and two 3's (two so that the 9 is covered). This minimum
set of factors multiplies to 
.
Therefore, the answer is (B).
A side note: since the factors of 315 happen to be prime
numbers (with the 9 counted as two 3's), we have found the prime factorization
of 315. Repeatedly dividing a number in order to get its prime factorization is
a technique always to keep in mind when confronting confusing situations around
multiplying, dividing, factors, and primes.
Again, the correct answer is (B).
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