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Tamanna is arranging black marbles in groups of 13 and purple marbles in groups of 25. If she has the same number of black and purple marbles, what is the smallest number of marbles of each colour that she could have?

Question

Tamanna is arranging black marbles in groups of 13 and purple marbles in groups of 25. If she has the same number of black and purple marbles, what is the smallest number of marbles of each colour that she could have?

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Solution

To solve this problem, we need to find the least common multiple (LCM) of 13 and 25. The LCM of two numbers is the smallest number that is a multiple of both numbers.

Here are the steps to find the LCM of 13 and 25:

  1. Write down the multiples of 13 and 25 until we find a common multiple.

Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325...

Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325...

  1. The smallest number that appears in both lists is 325.

So, the smallest number of marbles of each color that Tamanna could have is 325.

This problem has been solved

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