Question

Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12. $\left[3\text{Marks}\right]$

Answer 1

The least common multiple (LCM) of 2 or more numbers is the smallest number that they all divide evenly.

LCM:

$\begin{array}{cc}2& 6,8,12\\ 2& 3,4,6\\ 2& 3,2,3\\ 3& 3,1,3\\ & 1.1,1\end{array}$

LCM of 6, 8 and 12 = $2\times 2\times 2\times 3$ = 24 $\left[1\text{Mark}\right]$

The smallest 3-digit number = 100
To find the smallest 3-digit number possible we have to look for smallest 3-digit multiples of 24. $\left[0.5\text{Marks}\right]$

Multiples of 24 = 24, 48, 72, 96, 120, 144... $\left[0.5\text{Marks}\right]$

Clearly, 120 is the smallest 3-digit multiple of 24.
Therefore, the required number is 120. $\left[1\text{Mark}\right]$