Sharon's Sweets sells doughnuts in packages of 10. Across town, Lewis Pastries sells doughnuts in packages of 2. If Quinn wants to buy the same number of doughnuts from each bakery for a taste test, what is the smallest number of doughnuts she will have to buy from each?
Question
Sharon's Sweets sells doughnuts in packages of 10. Across town, Lewis Pastries sells doughnuts in packages of 2. If Quinn wants to buy the same number of doughnuts from each bakery for a taste test, what is the smallest number of doughnuts she will have to buy from each?
Solution
To find the smallest number of doughnuts Quinn has to buy from each bakery, we need to find the least common multiple (LCM) of the package sizes. The LCM of 10 and 2 is the smallest number that is a multiple of both numbers.
Step 1: List the multiples of each number.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Step 2: Find the smallest number that appears in both lists.
The smallest number that is a multiple of both 10 and 2 is 10.
So, Quinn will have to buy at least 10 doughnuts from each bakery for the taste test.
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