a rectangular cardboard, 15 cm by 50 cm is cut into smaller squares. What is the least number of such square pieces?
GCD(15,50) = 5
so, (15/5)(50/5) = 3*10 = 30
To find the least number of square pieces that can be cut from a rectangular cardboard, you need to determine the largest square that can fit into the cardboard without exceeding its dimensions.
In this case, the dimensions of the cardboard are 15 cm by 50 cm. To find the largest square that can fit into the cardboard, you need to find the greatest common divisor (GCD) of the two side lengths.
The GCD of 15 and 50 can be found using the Euclidean algorithm:
Step 1: Divide 50 by 15. The quotient is 3 and the remainder is 5.
Step 2: Divide 15 by 5. The quotient is 3 and the remainder is 0.
Step 3: The GCD is the last nonzero remainder, which is 5.
Therefore, the GCD of 15 and 50 is 5. This means that the largest square that can fit into the cardboard is a square with a side length of 5 cm.
To find the least number of such square pieces, you need to divide the length and width of the cardboard by the side length of the square.
Dividing 15 cm by 5 cm gives us 3, and dividing 50 cm by 5 cm gives us 10. This means that we can cut 3 squares along the 15 cm side and 10 squares along the 50 cm side.
Therefore, the least number of square pieces that can be cut from the rectangular cardboard is 3 x 10 = 30 square pieces.