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.