# Determine the largest 3-digit number which is exactly divisible by 8, 10 and 12.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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

STEP 1: By using the division method, find the L.C.M. of 8, 10, and 12. We determine the LCM of 8, 10, and 12 using the division method.

• L.C.M. of 8, 10 and 12 = 2 x 2 x 2 x 3 x 5 = 23 x 3 x 5
• L.C.M. of 8, 10 and 12 = 8 x 3 x 5 = 120

STEP 2: determining the biggest three-digit number that is 120 times larger

We are aware that 999 is the largest 3-digit number.

999 divided by 120 yields

999 = 120 x 8 + 39

The greatest three-digit number which is a multiple of 120 can be obtained by subtracting the remainder from 999.

120 x 8 = 999 – 39 = 960

The greatest three-digit number that is a multiple of 120 is 960, for example. 960 is the greatest three-digit number that can be divided into 8, 10, and 12 perfectly.

Summary:

### Determine the largest 3-digit number which is exactly divisible by 8, 10, and 12.

960 is the greatest three-digit number that is precisely divisible by 8, 10, and 12. The value which divides three given numbers can be found using the long division method. LCM is the least common multiple among all the given multiples.

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