Question

What is the LCM of 24a^3 b and 36ab ^2

Answer 1

72a^3b^2

Explanation:

The LCM is the number divisible by both numbers, multiples of 24 are 24,48,72 etc 36 is 36,72,108 etc the least I'd 72. with exponents it's the highest exponent because a^3 is a*a*a

Answer 2

Answer: Last Option

`72a^3b^2`

Explanation:

We look for the LCM between
`24a^3 b` and
`36ab ^2`

First find the prime factors of 24 and 36

24 | 2

12 | 2

6 | 2

3 | 3

1

`24=2^3*3`

36 | 2

18 | 2

9 | 3

3 | 3

1

`36=2^2 * 3^2`

Then we have:

`2^3*3a^3b` and
`2^2 * 3^2ab^2`

Now we choose the common and uncommon factors raised to the greatest exponent

`LCM(2^3*3a^3b,\ 2^2 *3^2ab^2)=2^3(3^2)a^3b^2\\\\LCM(2^3*3a^3b,\ 2^2 * 3^2ab^2) =72a^3b^2`