Question

Which smallest 3-digit number is divisible by 12, 18 and 24?​

Answer 1

Answer:

The Smallest number exactly divisible by 6, 8 and 12

Let us determine the LCM of 6, 8, 1 2

Common Multiples of 6: 6,12,18,24,30,36,42…..

Common Multiples of 8: 8,16,24,32,40,48,54……

Common Multiples of 12: 12,24,36,48,60,72,…

We note that 2 4 is the least common multiple of 6,8 and 12

We have to find the smallest 3 -digit multiple of 24.

Also 24 × 4 = 96 and 24 ×5 = 120.

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

Answer 2

Given:

To find the smallest 3-digit number is divisible by 12, 18 and 24?.

Solution:

Understand that the LCM of two or more than two numbers, is a smallest number that is divisible by that numbers.

Find the LCM of 12,18 and 24,

$\[\begin{array}{l} = 6 \times 2,6 \times 3,6 \times 4\\ = 6 \times 4 \times 3\\ = 72\end{array}\]$

Therefore the LCM of  12,18 and 24 is 72,

Find the smallest 3-digit number is divisible by 12, 18 and 24,

$\[\begin{array}{l} = 2 \times 72\\ = 144\end{array}\]$

Hence, 144 is the smallest 3-digit number is divisible by 12, 18 and 24.