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Shivani's Blossoms sells roses in groups of 3. Across town, Lisa's Blooms sells roses in groups of 7. If a customer wants to buy the same number of roses from both vendors, what is the smallest number of roses the customer will have to buy from each vendor?

Question

Shivani's Blossoms sells roses in groups of 3. Across town, Lisa's Blooms sells roses in groups of 7. If a customer wants to buy the same number of roses from both vendors, what is the smallest number of roses the customer will have to buy from each vendor?

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Solution

To find the smallest number of roses a customer has to buy from each vendor, we need to find the least common multiple (LCM) of 3 and 7, which are the group sizes the vendors sell in.

Step 1: List the multiples of each number.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60...

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140...

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

The smallest number that both lists share is 21.

So, the customer will have to buy at least 21 roses from each vendor to have the same number of roses from both.

This problem has been solved

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