Question

John has two pieces of rope, one is 18 meters long and the other is 15 meters long. He wants to cut them into smaller pieces of equal length without any rope left over. How many pieces will he have in total?

• A. 11
• B. 12
• C. 10
• D. 9

Hint:

For cutting into equal pieces without leftover, find the GCD of lengths and divide each by it.

Answer 1

The Correct Option is A

Step 1: Understanding the problem
John wants to cut two ropes (18 m and 15 m) into smaller pieces, all equal length, with no leftover pieces.
Step 2: Find the maximum length of each piece
To cut both ropes into equal-length pieces without leftover, the length must be a common divisor of both 18 and 15. The largest such length is the Greatest Common Divisor (GCD).
Step 3: Calculate the GCD of 18 and 15
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 15: 1, 3, 5, 15
Common factors: 1, 3
Largest common factor = 3
Step 4: Calculate the number of pieces
- Number of pieces from 18 m rope = 18 ÷ 3 = 6
- Number of pieces from 15 m rope = 15 ÷ 3 = 5
Step 5: Total pieces
6 + 5 = 11 pieces
Hence, the answer is 11 pieces in total.