Question

Anirudh wants to cut a large rectangular board into small identical square pieces. If the board size is 18 inches by 30 inches,
What is the least number of square pieces he can cut without wasting any of the board?​

Answer 1

Answer:

. We find Greatest Common Factor of 18 and 30. GCF(18, 30) = 6.

18 = 6 × 3

30 = 6 × 5

Hence the least number of square pieces is: 3 × 5 = 15

* Therefore, the least number of square pieces are 15.

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Answer 2

Answer:

The least number of square that can be cut out without wasting any of the board is 15.

Step-by-step explanation:

Length of rectangle = 30 inches

Breadth of rectangle = 18 inches

G.C.D (Greatest common divisor) of 18 and 30,

⇒ G.C.D(18,30) = 6

Thus, 6 divides both 18 and 30.

This implies 6 must be the side of each square that can be cut out without wasting any of the board.

Side of square, $a$ = 6 inches

Let $n$ be the number of squares.

Area of rectangle = $n$ × Area of square

⇒ Length × breadth = $n$ × $a^2$

⇒ 30 × 18 = $n$ × 6 × 6

⇒ $n$ = $\frac{30 \cdot 18}{6 \cdot6}$

⇒ $n=15$

Therefore, 15 is the least number of square that can be cut out without wasting any of the board.

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