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What is the least common multiple (LCM) of 12 and 15?

Practice Questions

Q1
What is the least common multiple (LCM) of 12 and 15?
  1. 30
  2. 60
  3. 90
  4. 120

Questions & Step-by-Step Solutions

What is the least common multiple (LCM) of 12 and 15?
Correct Answer: 60
  • Step 1: Find the prime factorization of 12. The prime factors are 2 and 3. So, 12 = 2^2 * 3.
  • Step 2: Find the prime factorization of 15. The prime factors are 3 and 5. So, 15 = 3 * 5.
  • Step 3: List all the prime factors from both numbers, using the highest power of each. We have 2^2 from 12, 3^1 from both, and 5^1 from 15.
  • Step 4: Multiply these together to find the LCM. So, LCM = 2^2 * 3^1 * 5^1.
  • Step 5: Calculate the multiplication: 2^2 = 4, then 4 * 3 = 12, and finally 12 * 5 = 60.
  • Step 6: Therefore, the least common multiple (LCM) of 12 and 15 is 60.
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