Question

Find the LCM of $ab^2c^2, a^2bc$ and $a^3b^3c^2$.

• A. $$a^3b^3c^2$$
• B. $$abc$$
• C. $$a^2b^2c^2$$
• D. $$a^3b^3c^3$$

Answer 1

Answer:

$$a^3b^3c^2$$

List the prime factors for each term:

$a b ^ 2 c ^ 2 = a ^ 1 b ^ 2 c ^ 2$

$a ^ 2 bc = a ^ 2 b ^ 1 c ^ 1$

$a ^ 3 b ^ 3 c ^ 2 = a ^ 3 b ^ 3 c ^ 2$

For each variable, take the highest power appearing in any term:

For $a : a ^ 3 , b : b ^ 3, c : c ^ 2$

Multiply these highest powers together to get the LCM:

LCM = $a^3b^3c^2$