What pair of numbers has an LCM of 60?

Steps to Solve

1. Identify pairs of numbers Start by identifying pairs of numbers that could potentially have an LCM of 60. We can consider pairs such as (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10).

2. Calculate the LCM for each pair Use the LCM formula to calculate the LCM of each pair. The LCM of two numbers $a$ and $b$ can be calculated using the formula: $$ LCM(a, b) = \frac{|a \cdot b|}{GCD(a, b)} $$ where GCD is the greatest common divisor.

3. Evaluate each pair For each pair, calculate the LCM:

• For (1, 60):

  • $GCD(1, 60) = 1$
  • $LCM(1, 60) = \frac{|1 \cdot 60|}{1} = 60$

• For (2, 30):

  • $GCD(2, 30) = 2$
  • $LCM(2, 30) = \frac{|2 \cdot 30|}{2} = 30$

• For (3, 20):

  • $GCD(3, 20) = 1$
  • $LCM(3, 20) = \frac{|3 \cdot 20|}{1} = 60$

• For (4, 15):

  • $GCD(4, 15) = 1$
  • $LCM(4, 15) = \frac{|4 \cdot 15|}{1} = 60$

• For (5, 12):

  • $GCD(5, 12) = 1$
  • $LCM(5, 12) = \frac{|5 \cdot 12|}{1} = 60$

• For (6, 10):

  • $GCD(6, 10) = 2$
  • $LCM(6, 10) = \frac{|6 \cdot 10|}{2} = 30$

4. Find valid pairs From the calculations, the pairs whose LCM is 60 are (1, 60), (3, 20), (4, 15), and (5, 12).