What is the least common multiple (LCM) of 12 and 15?
Practice Questions
1 question
Q1
What is the least common multiple (LCM) of 12 and 15?
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60
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120
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.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the least common multiple (LCM) of 12 and 15?
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.
Steps: 6
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.
