Question

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

Answer 1

Answer: Last Option

$72a^3b^2$

Step-by-step 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

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

Answer 2

Answer:

72a^3b^2

Step-by-step 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