How do i find the lcm

Question

Qn: If the product of two integers is $2^7 \cdot 3^8 \cdot 5^2 \cdot 7^{11}$ and their greatest common divisor is $2^3 \cdot 3^4 \cdot 5$, what is their least common multiple?

I have issue with this question please help me solve it.

I tried assuming that lcm is $x$ =. Then, Gcd $\cdot x = 2^3 \cdot 3^4 \cdot 5x$. And, product factors /Gcd $x$

Answer 1

The product of two integers is the gcd times the lcm. You can demonstrate that by considering the prime factorizations of each. The gcd gets the minimum exponent of the two numbers and the lcm gets the maximum.