The least common multiple of two positive integers is 7!, and their greatest common divisor is 9. If one of the integers is 315, then what is the other?

Let the other number = N

GCD[N, 315] = 9, solve for N

N = 9

LCM[N, 315] =7!, solve for N

N = 16

So, in order to satisfy both GCD and LCM, then:

N = 9 x 16 = 144, so that:

GCD[144, 315] = 9, and

LCM[144, 315] =7!, So;

N = 144 - the second number.