Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12

Solution:

We will be using the concept of LCM(Least Common Multiple) to solve this.

We know that the smallest 3-digit number is 100

Let's find the LCM of 6, 8, and 12 as shown below.

As we can observe from the division method, LCM of 6, 8, and 12 is 2 × 2 × 2 × 3 = 24

Thus, all the multiples of 24 will also be divisible by 6, 8, and 12.

Now we will divide the smallest-3 digit number with the LCM obtained, and the remainder will be subtracted from the dividend, and 24 will be added to it to make it perfectly divisible.

Let us observe below.

So, the smallest three digit multiple of 24 will be,

100 = (100 – 4) + 24 = 96 + 24 = 120

Hence, the smallest 3-digit number which is exactly divisible by 6, 8, and 12, is 120.

You can also use the LCM Calculator to solve this.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 Question 4

Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12

Summary:

The smallest 3-digit number which is exactly divisible by 6, 8, and 12, is 120.

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