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

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

Options:

  1. 30
  2. 60
  3. 90
  4. 120

Correct Answer: 60

Solution: 

The LCM of two numbers is found by taking the highest power of each prime factor. The prime factorization of 12 is 2^2 * 3 and for 15 is 3 * 5. Thus, LCM = 2^2 * 3 * 5 = 60.

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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