Question

A bag of mangoes are packed into small boxes that can contain 12, 24, and 30 mangoes. Find the minimum number of mangoes in the bag ....give answers

Answer 1

Given:

A bag of mangoes is packed into small boxes which can contain 12, 24 and 30 mangoes respectively.  

To find:

Find the minimum number of mangoes in the bag.

Solution:

From the given information, we have the data as follows.

The minimum number of mangoes in the bag is equal to the LCM of 12, 24 and 30 mangoes.

From the given information, we have the data as follows.

Prime Factorization of 12 is:

2 × 2 × 3  ⇒  2² × 3¹

Prime Factorization of 24 is:

2 × 2 × 2 × 3  =>  2³ × 3¹

Prime Factorization of 30 is:

2 × 3 × 5  =>  2¹ × 3¹ × 5¹

Therefore, the LCM of 12, 24 and 30 is calculated as follows.

LCM = 2³ × 3¹ × 5¹ = 120

Therefore, the minimum number of mangoes in the bag is 120.