Two numbers are $a=x^4{y}^2{z}^3$ and $b=x^2{y}^{5}z$, where $x,y$ and $z$ are distinct primes.
What is LCM(a, b)?

For the LCM take the HIGHEST power of each prime that appears: $x$ to the power max(4, 2) = $x^4,y$ to the power max(2, 5) = $y^5,z$ to the power max(3, 1) = $z^3$. So LCM = $x^4{y}^5{z}^3$. Taking the lowest powers gives the HCF, $x^2{y}^{2}z$; adding the exponents gives $x^6{y}^7{z}^4$, which is the product a $x$ b, not the LCM.