Question

Find the greatest number of five digits exactly divisible by 9, 12, 15, 18 and 24.

Answer 1

First, we will find the LCM of 9, 12, 15, 18 and 24.
$\begin{array}{l}2\overline{)9,12,15,18,24}\\ 2\overline{)9,6,15,9,12}\\ 2\overline{)9,3,15,9,6}\\ 3\overline{)9,3,15,9,3}\\ 3\overline{)3,1,5,3,1}\\ \text{5}\overline{)\text{1,1,5,1,1}}\\ \text{1,1,1,1,1}\\ \\ {\text{∴ LCM of the numbers = 2}}^3{\text{× 3}}^2\text{× 5}\\ \text{= 360}\\ \text{The least six-digit number = 100000}\\ \text{The greatest five-digit number divisible by 360}\\ \text{will be the quotient of}\frac{100000}{360}\text{mutiplied by 360.}\\ 360\begin{array}{c}277\\ \overline{)100000}\end{array}\\ \frac{720}{\begin{array}{l}2800\\ \frac{2520}{280}\end{array}}\\ \\ \text{So, the greatest five-digit number exactly divisible}\\ \text{by the given numbers will be}\\ \text{360}\times \text{277 = 99720}\end{array}$