Determine the Smallest 3-digit Number Which is Exactly Divisible by 6, 8, and 12

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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

Smallest three digits number.

First, we have to find the LCM of given numbers that is 6, 8, and 12.

Multiples of 6, 8, and 12 are

Common Multiples of 6 = 6, 12, 18, 24, 30, 36, …..

Common Multiples of 8 = 8, 16, 24, 32, 40, ….

Common Multiples of 12 = 12, 24, 36, 48, 60, …..

It is observed that, 24 is the least common multiple.

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

The lowest three-digit number will now be divided using the calculated LCM, the remainder will be deducted from the dividend, and 24 will be added to it to make the number perfectly divisible.

100/24 = 4 Remainder = 4

According to the above statement.

= (100 – 4) + 24

= 96 + 24

= 120

Table of content

1. Determine the Smallest 3-digit Number Which is Exactly Divisible by 6, 8, and 12

Multiples

A multiple is the outcome of multiplying an integer (not a fraction) by a certain number. By subtracting the product of counting numbers and whole numbers, the multiples of the whole number are obtained. For instance, we multiply 6 by 1, 6 by 2, 6 by 3, and so forth to discover the multiples of 6. The result of this multiplication is the multiples.

List of Multiples of Numbers

Since multiples of a number are created by multiplying it by natural numbers, a number can have an unlimited number of multiples. So, for a given integer, we can write an unlimited number of multiples.

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