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During a trip to the beach, Rafi built sandcastles with 2 towers each, and Monica built sandcastles with 15 towers each. Before leaving, they counted the towers and realized that they had each built the same number. What is the smallest number of towers each must have built?

Question

During a trip to the beach, Rafi built sandcastles with 2 towers each, and Monica built sandcastles with 15 towers each. Before leaving, they counted the towers and realized that they had each built the same number. What is the smallest number of towers each must have built?

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Solution

To find the smallest number of towers each must have built, we need to find the least common multiple (LCM) of the number of towers in the sandcastles they each built. Rafi built sandcastles with 2 towers each and Monica built sandcastles with 15 towers each.

Step 1: List the multiples of each number until you find a common multiple.

Multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150...

Multiples of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150...

Step 2: Identify the least common multiple.

The least common multiple of 2 and 15 is 30.

So, the smallest number of towers each must have built is 30.

This problem has been solved

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