What is the least common multiple of 15, 34, and 55?
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To find the least common multiple (LCM) of 15, 34, and 55, we need to determine the smallest number that is divisible by all three of these numbers. Here's how you can find the LCM:
1. Find the prime factorization of each number:
- Prime factorization of 15: 3 × 5
- Prime factorization of 34: 2 × 17
- Prime factorization of 55: 5 × 11
2. Identify the highest power of each prime factor that appears in any of the numbers:
- The highest power of 2 is 1 (2 is only a factor of 34).
- The highest power of 3 is 1 (3 is only a factor of 15).
- The highest power of 5 is 1 (5 appears in 15 and 55).
- The highest power of 11 is 1 (11 is only a factor of 55).
- The highest power of 17 is 1 (17 is only a factor of 34).
3. Multiply the factors found in step 2 to obtain the LCM: LCM = 2 × 3 × 5 × 11 × 17 = 5610.
So, the least common multiple of 15, 34, and 55 is 5610.