Question

A rabbit is packing lunches for his children he has 90 carats and 72 leaves of lettuce if he is giving each bunny the same number of carrots in the same number of lease of lettuce how many baby bunnies must he have he will have no extra vegetables after he packs the lunches A 6 B 18 C 9 D 3

Answer 1

To find out how many baby bunnies the rabbit has, we need to determine the greatest common divisor (GCD) of 90 carrots and 72 leaves of lettuce. The GCD will give us the maximum number of bunnies that can get an equal share of both carrots and lettuce without any leftovers.

Let's find the GCD of 90 and 72:

1. **Prime factorization**:
- 90 = 2 × 3^2 × 5
- 72 = 2^3 × 3^2

2. **Identify the common prime factors**:
- The common factors are:
- For 2: min(1, 3) = 1
- For 3: min(2, 2) = 2
- For 5: min(1, 0) = 0 (not common)

3. **Calculating GCD**:
- GCD = 2^1 × 3^2 = 2 × 9 = 18

The rabbit can divide the carrots and lettuce among 18 bunnies without any leftovers.

So the answer is **B) 18**.