Questions: Assessment Practice 24. Match each pair of numbers with the pair of numbers that has the same LCM. Same LCM as 6,8: 4,10; 5,8; 8,20

Assessment Practice 24. Match each pair of numbers with the pair of numbers that has the same LCM. Same LCM as 6,8: 4,10; 5,8; 8,20
Transcript text: Assessment Practice 24. Match each pair of numbers with the pair of numbers that has the same LCM. Same LCM as 6,8: 4,10; 5,8; 8,20
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Solution

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Solution Steps

Step 1: Calculate LCM for Each Pair

We calculate the Least Common Multiple (LCM) for the given pairs of numbers:

  • For \( (6, 8) \): \( \text{LCM}(6, 8) = 24 \)
  • For \( (4, 10) \): \( \text{LCM}(4, 10) = 20 \)
  • For \( (5, 8) \): \( \text{LCM}(5, 8) = 40 \)
  • For \( (8, 20) \): \( \text{LCM}(8, 20) = 40 \)
Step 2: Identify Pairs with the Same LCM

Next, we identify which pairs share the same LCM:

  • The pairs \( (5, 8) \) and \( (8, 20) \) both have an LCM of \( 40 \).
  • The pairs \( (6, 8) \) and \( (4, 10) \) have unique LCMs of \( 24 \) and \( 20 \), respectively.

Final Answer

The pairs that have the same LCM are \( (5, 8) \) and \( (8, 20) \) with \( \text{LCM} = 40 \). Thus, the answer is:

\(\boxed{(5, 8) \text{ and } (8, 20) \text{ have the same LCM of } 40}\)

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