Rahim wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?

Question: Rahim wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?

Solution:
To get the least number of square pieces, each square must be as large as possible.
So, the side of each square will be the GCF of 18 and 30.
18 = 2 × 3²
30 = 2 × 3 × 5

∴ GCF = 2 × 3 = 6

So, each square has side 6 inches.

∴ Number of square pieces = (18/6) × (30/6)
= 3 × 5
= 15

Correct Answer: ঘ) 15