Question

Write a 3-digit number that is divisible by both 3 and 4. Explain how you know this number is divisible by 3 and 4.

Answer 1

A number is divisible by 3 if the sum of all the digits are a multiple of 3
A number is divisible by 4 if the last two digits are a multiple of 4
Therefore 12 is a number divisible by both 3 and 4 according to their rules


Hope this helped you

Answer 2

Concept

The rules for divisibility of 3 are as follows: If the sum of the digits of a number is divisible by 3, then the number is also divisible by 3.

The rule of divisibility of 4 is that if the last two digits of a number are divisible by 4, the number is a multiple of 4 and is divisible by 4.

Given

We have given two numbers 3 and 4.

Find

We are asked to determine a 3-digit number that is divisible by both 3 and 4.

Solution

To be divisible by 3 and 4, the required number must be divisible by the least common multiple or the LCM of 3 and 4. This is 12. So you need to take an integer multiple of 12 and see what the 3-digit number is. Since 100 is the smallest 3-digit number, it must be a multiple greater than 100.

$12\times9=108\\12\times10=120$

Therefore, 108,120....are the 3-digit number is which is divisible by both 3 and 4.

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