Question

Determine the largest 3-digit number which is exactly divisible by 8, 10 and 12.
[5 marks]

Answer 1

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

LCM of 8, 10, 12:

$\begin{array}{cc}2& 8,10,12\\ 2& 4,5,6\\ 2& 2,5,3\\ 3& 1,5,3\\ 5& 1,5,1\\ & 1,1,1\end{array}$
[2 marks]

LCM of 8, 10, 12 = $2\times 2\times 2\times 3\times 5$ = 120
[0.5 mark]

The largest three digit number = 999
[0.5 mark]

Now,


Therefore, the required number = 999 – 39 = 960
[1.5 marks]