Two brands of chocolates are available in pack of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?

Question

Answer

The LCM of 24 and 15

Now, 24 = 2 * 2 * 2 * 3

and 15 = 3 * 5

LCM(24, 15) = 2 * 2 * 2 * 3 * 5 = 120

Now, the number of boxes of pack of 24 = 120/24 = 5

and the number of boxes of pack of 15 = 120/15 = 8

Answer

Solution:

Finding the common factor

To find the least number of boxes of each kind, we need to find the common factor of 24 and 15.

- The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
- The factors of 15 are 1, 3, 5, and 15.

The common factor of 24 and 15 is 3.

Calculating the number of boxes

To calculate the number of boxes of each kind we need to buy, we divide 24 and 15 by 3.

- 24 ÷ 3 = 8 boxes of the first kind
- 15 ÷ 3 = 5 boxes of the second kind

Therefore, we need to buy 8 boxes of the first kind and 5 boxes of the second kind to have an equal number of chocolates of both kinds.

Explanation

When we buy 8 boxes of the first kind, we get 8 x 24 = 192 chocolates.

When we buy 5 boxes of the second kind, we get 5 x 15 = 75 chocolates.

Since 192 and 75 are both multiples of 3, we can divide both numbers by 3 to get an equal number of chocolates from both kinds.

Therefore, we need to buy 8 boxes of the first kind and 5 boxes of the second kind to have an equal number of chocolates of both kinds.

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