Question
Find the least common multiple (LCM) of 4 and 6
Ask by Marshall Ray. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The least common multiple (LCM) of 4 and 6 is 12.
Solution
To find the LCM of 4 and 6, we first factor each number into its prime factors:
• 4 = 2²
• 6 = 2 × 3
Next, take the highest power of each prime that appears in either factorization:
• For 2: the highest power is 2²
• For 3: the highest power is 3¹
Multiply these together:
LCM = 2² × 3 = 4 × 3 = 12
Thus, the least common multiple (LCM) of 4 and 6 is 12.
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Simplify this solution Mind Expander
The least common multiple (LCM) of 4 and 6 is 12. To find this, you can list the multiples of each number: the multiples of 4 are 4, 8, 12, 16, and so on, while the multiples of 6 are 6, 12, 18, and so on. The smallest multiple they share is 12, making it the LCM! To break it down further, you can also use the prime factorization method. The prime factorization of 4 is 2², and for 6, it's 2¹ × 3¹. To find the LCM, you take the highest power of each prime: 2² and 3¹. Multiply these together (2² × 3¹ = 4 × 3 = 12), and voilà! You've got your LCM.
