What are the first three common multiples of 6 and 8, and also the first three common multiples of 12 and 18?

To find the first three common multiples of the given pairs of numbers, we start by determining the least common multiples (LCM) for each set.

Finding Common Multiples of 6 and 8

1. **Identify the multiples:**

  • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, …
  • Multiples of 8: 8, 16, 24, 32, 40, …

2. **Find the common multiples:**

  • The first common multiple is 24.
  • The next common multiple is 48.
  • The third common multiple is 72.

Thus, the first three common multiples of 6 and 8 are 24, 48, and 72.

Finding Common Multiples of 12 and 18

1. **Identify the multiples:**

  • Multiples of 12: 12, 24, 36, 48, 60, …
  • Multiples of 18: 18, 36, 54, 72, …

2. **Find the common multiples:**

  • The first common multiple is 36.
  • The next common multiple is 72.
  • The third common multiple is 108.

Thus, the first three common multiples of 12 and 18 are 36, 72, and 108.

Summary

To summarize, the first three common multiples are:

  • For 6 and 8: 24, 48, 72
  • For 12 and 18: 36, 72, 108

These multiples reflect the smallest numbers that can be evenly divided by the original pairs of numbers, making them very useful in various mathematical applications.

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