The lengths of three wires were 30m, 36 m and 84m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained.
LCF of 30,36,84 is 6
so if we make 5 cuts of 6 m from the smallest
6 cuts from the 2nd
and 14 pieces from the third for a total of 25 pieces
God of 30,36 and 84 is 6.
30/6 is 5
36/6 is 6
84/6 is 14
Number of pieces obtained is 5+6+14=25
LCM of 30,36,84=6
30/6=5
36/6=6
84/6=14
Therefore the total pieces are
5+6+14=25 pieces
30- 2×3×5
36- 2²×3²
84- 2²×3×7
GCD - 2×3
Pieces obtained. (30÷6)+ (36÷6) + (84÷6)
5+6+14= 25 pieces.
To find the least number of equal-sized pieces that can be obtained from three wires, we need to find the greatest common divisor (GCD) of the lengths of the wires.
Step 1: Find the GCD of the three wire lengths.
We can use the Euclidean algorithm to find the GCD.
First, find the GCD of the smallest two wire lengths: 30m and 36m.
GCD(30, 36) = 6
Now, find the GCD of the result from the previous step (6) and the remaining wire length: 84m.
GCD(6, 84) = 6
Therefore, the GCD of the three wire lengths is 6.
Step 2: Calculate the number of equal-sized pieces.
To calculate the number of equal-sized pieces, we need to divide the lengths of the wires by the GCD.
For the first wire: 30m ÷ 6m = 5 pieces
For the second wire: 36m ÷ 6m = 6 pieces
For the third wire: 84m ÷ 6m = 14 pieces
Step 3: Find the least number of pieces obtained.
To find the least number of pieces obtained, we take the minimum value among the three calculations.
Therefore, the least number of pieces obtained is 5 pieces.
Why did the wire go to therapy?
Because it needed to find its "lengths" and work through some "cuts"!
Now, let's figure out the least number of pieces obtained. We can start by finding the greatest common divisor of the given lengths:
30 = 2 × 3 × 5,
36 = 2 × 2 × 3 × 3, and
84 = 2 × 2 × 3 × 7.
So, the common factors are 2 and 3. The smallest possible length that can be cut from all three wires would then be 2 × 3 = 6.
To calculate the least number of pieces, we divide each wire length by 6:
30 ÷ 6 = 5 pieces,
36 ÷ 6 = 6 pieces, and
84 ÷ 6 = 14 pieces.
Therefore, the least number of pieces obtained would be 5.