A piece of rope can be cut into an exact number of 6 m lengths. The rope could also be cut into an exact number of 8 m lengths. What is the shortest possible length of the rope
In order to find the shortest possible length of the rope, we need to find the smallest common multiple of 6 and 8.
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48...
The multiples of 8 are: 8, 16, 24, 32, 40, 48...
From the lists above, we can see that the smallest common multiple of 6 and 8 is 24.
Therefore, the shortest possible length of the rope is 24 meters.
To find the shortest possible length of the rope, we need to find the least common multiple (LCM) of 6 and 8.
Step 1: Find the prime factors of each number:
- 6 can be written as 2 x 3
- 8 can be written as 2 x 2 x 2
Step 2: Find the highest power of each prime factor:
- The highest power of 2 is 3 (from 8)
- The highest power of 3 is 1 (from 6)
Step 3: Multiply the prime factors with their highest powers:
- 2^3 x 3^1 = 8 x 3 = 24
Therefore, the shortest possible length of the rope is 24 meters.