Question

find the least common multiple of these two expressions. $8y^{6}w^{3}$ and $20v^{7}y^{5}w^{2}$

Explanation:

Step1: Factor coefficients to primes

$8 = 2^3$, $20 = 2^2 \times 5$

Step2: Take max prime exponents

For 2: $\max(3,2)=3$; For 5: $\max(0,1)=1$
Coefficient LCM: $2^3 \times 5 = 40$

Step3: Take max $v$ exponents

$\max(0,7)=7$, so $v^7$

Step4: Take max $y$ exponents

$\max(6,5)=6$, so $y^6$

Step5: Take max $w$ exponents

$\max(3,2)=3$, so $w^3$

Step6: Multiply all LCM parts

$40 \times v^7 \times y^6 \times w^3$

Answer:

$40v^7y^6w^3$