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Chad's Sweets sells doughnuts in packages of 15. Across town, Mercer Pastries sells doughnuts in packages of 4. If Eve 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

Chad's Sweets sells doughnuts in packages of 15. Across town, Mercer Pastries sells doughnuts in packages of 4. If Eve 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?

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Solution

To solve this problem, we need to find the least common multiple (LCM) of 15 and 4. The LCM is the smallest number that is a multiple of both numbers.

Step 1: List the multiples of each number.

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300...

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120...

Step 2: Find the smallest number that appears in both lists.

The smallest number that is a multiple of both 15 and 4 is 60.

So, Eve will have to buy 60 doughnuts from each bakery.

This problem has been solved

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