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# Determine the greatest 3-digit number exactly divisible by 8, 10 and 12

**Solution:**

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

To determine the greatest 3-digit number exactly divisible by 8, 10, and 12, we need to find the LCM of the given numbers.

Let's find the LCM of 8, 10, and 12 as shown below.

LCM of 8, 10, and 12 will be equal to 2 × 2 × 2 × 3 × 5 = 120

As we know that the greatest 3-digit number is 999, we will now divide 999 by the obtained LCM that is 120.

Since the remainder is not 0, hence we subtract 39 from 999.

999 - 39 = 960 which is a multiple of 120 and is exactly divisible.

Now,

120 × 8 = 960 and 120 × 9 = 1080.

We see that 120 × 9 = 1080 is a 4-digit number but, we need the greatest 3-digit multiple.

Therefore, the greatest 3-digit multiple of 120 is 120 × 8 = 960 i.e, 960.

Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.

You can also use the LCM Calculator to solve this.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 Question 5

## Determine the greatest 3-digit number exactly divisible by 8, 10 and 12

**Summary:**

The greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.

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