If the students of a class can be grouped into 6 or 8 or 10, then find the minimum number of students, which must be in the class.

Given :

The students of a class can be grouped into 6 or 8 or 10.

To do :

We have to find the minimum number of students that must be in the class.

Solution :

Let the number of students in the class be x.

This implies,

x must be divisible by 6, 8, and 10 completely.

Therefore, we have to find the LCM of 6,8 and 10.

Prime factorisation of 6,8 and 10 is,

$6 = 2\times 3$

$8 = 2\times 2\times 2$

$10 = 2\times 5$

LCM of 6, 8 and 10 $= 3\times 2\times 2\times 2\times 5 = 3\times 8\times 5 = 24\times 5 = 120$.

The minimum number of students that must be in the class that can be grouped into 6 or 8 or 10 is 120.

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Updated on: 10-Oct-2022

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