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?
Formula:
\(\begin{array}{|rcll|} \hline GCD(M, N) \times LCM(M, N) &=& M \times N \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline GCD(M, N) \times LCM(M, N) &=& M \times N \\ 9\times 7! &=& 315\cdot N \\\\ N &=& \dfrac{9\times 7!}{315} \\\\ &=& \dfrac{ 7!}{35} \\\\ &=& \dfrac{ 2\times 3 \times 4 \times 5 \times 6 \times 7 }{5\times 7} \\\\ &=& 2\times 3 \times 4 \times 6 \\\\ &=& 144 \\ \hline \end{array} \)
The other is 144