To find the least common multiple (LCM) of 6 and 15, you can follow these steps:
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List the prime factors:
- The prime factorization of 6 is: \(2 \times 3\)
- The prime factorization of 15 is: \(3 \times 5\)
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Identify the highest power of each prime factor:
- From the factorizations, we identify:
- The prime factor \(2\) appears in \(6\) (with a power of \(1\)).
- The prime factor \(3\) appears in both \(6\) and \(15\) (with a maximum power of \(1\)).
- The prime factor \(5\) appears in \(15\) (with a power of \(1\)).
- From the factorizations, we identify:
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Multiply the highest powers of each prime factor:
- LCM = \(2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5\)
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Calculate the LCM:
- \(2 \times 3 = 6\)
- \(6 \times 5 = 30\)
Thus, the least common multiple (LCM) of 6 and 15 is 30.