The least common multiple (LCM) of 51, 68, and 85 is 1020.
To find the LCM of these numbers, we can use the prime factorization method. Here’s how it works:
- Prime Factorization:
- 51 = 3 × 17
- 68 = 2² × 17
- 85 = 5 × 17
- Identify the Highest Powers: Take the highest power of each prime number that appears in the factorizations.
- 2² (from 68)
- 3 (from 51)
- 5 (from 85)
- 17 (common in all)
- Multiply the Highest Powers: Multiply these together to get the LCM.
- 2² × 3 × 5 × 17 = 4 × 3 × 5 × 17 = 1020
So, the LCM of 51, 68, and 85 is 1020.