This CBSE class 10 Maths Extra Question from the topic Real Numbers. This word problem tests your ability to decode that the question requires computing LCM to find the answer.

Question - 10 : 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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**Given**: Black marbles is arranged in group of 13.

Purple marbles is arranged in group of 25.

Tamanna is arranging black marbles in groups of 13.

So, the number of black marbles she has will be a **multiple of 13.**

She is arranging purple marbles in groups of 25.

So, the number of purple marbles she has will be a **multiple of 25.**

She has the same number of black and purple marbles.

i.e., the number of marbles of each colour that she has is a multiple of 13 and a multiple of 25.

Or the number of marbles of each colour that she has is a common multiple of 13 and 25.

Because we are finding the smallest number of marbles of each colour, we have to compute the lowest common multiple or the LCM of 13 and 25.

**Step 1**: Prime factorise 13 and 25

13 is a prime number.

25 = 5^{2}

**Step 2**: List down all primes in the two numbers

13 and 5 are prime numbers in the two numbers.

**Step 3**: LCM is the product of the greatest power of all primes in the 2 numbers.

LCM = 13 × 5^{2} = 13 × 25 = 325

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