least common multiple of 2ab^2 and 4ab
You asked:
Find the polynomial least common multiple of the following expressions: \(2 b^{2} a\), \(4 a b\)
MathBot Answer:
The least common multiple is \(4 b^{2} a\).
Begin by factoring all expressions completely. $$\begin{aligned}2 b^{2} a &= 2 \cdot b^{2} \cdot a\\4 a b &= 2^{2} \cdot a \cdot b\\\end{aligned}$$
Find the least common multiple by multiplying the factors together, including only the greatest power of each common factor. \[\operatorname{lcm}(2 b^{2} a, 4 a b) = 2^{2}\cdot (a)^{1}\cdot (b)^{2} = 4 b^{2} a\]