Lara wishes to advertise her business, so she gives packs of 6 red flyers to each restaurant owner and sets of 8 blue flyers to each clothing store owner. At the end of the day, Lara realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each colour?
Question
Lara wishes to advertise her business, so she gives packs of 6 red flyers to each restaurant owner and sets of 8 blue flyers to each clothing store owner. At the end of the day, Lara realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each colour?
Solution
To find the minimum number of flyers of each color that Lara gave out, we need to find the least common multiple (LCM) of 6 and 8.
Step 1: List the prime factors of each number.
- The prime factors of 6 are 2 and 3.
- The prime factors of 8 are 2, 2, and 2.
Step 2: Multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply it the greatest number of times it occurs.
- 2 occurs three times in 8 and once in 6, so we multiply it three times.
- 3 occurs once in 6 and does not occur in 8, so we multiply it once.
Step 3: Multiply the results from step 2 to get the LCM.
- 2 * 2 * 2 * 3 = 24
So, the minimum number of flyers of each color that Lara gave out is 24.
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