A rabbit is packing lunches for his children. He has 90 carrots and 72 leaves of lettuce. If he is giving each bunny the same number of carrots and the same number of leaves of lettuce, how many baby bunnies must he have? He will have no extra vegetables after he packs the lunches.(1 point)

Question

Responses

3
3

9
9

6
6

18

Answer 1

To find the number of baby bunnies, we need to find the greatest common divisor of the number of carrots and the number of leaves of lettuce. Let's find the prime factorization for both 90 and 72:

90 = 2 * 3^2 * 5
72 = 2^3 * 3^2

To find the greatest common divisor, we take the lowest exponent for each prime factor:

The exponent for 2 is 3 (from 72)
The exponent for 3 is 2 (from both 90 and 72)
The exponent for 5 is 0 (from 90)

Therefore, the greatest common divisor is 2^3 * 3^2 = 8 * 9 = 72. This means that the rabbit must have 72 baby bunnies.

So the correct answer is 18.