Question

Find the smallest number of the six digits divisible by $18,24$ and $30$.

Answer 1

To find the $LCM$ of $18,24$ and$30$ first we will write each one of them as the product of its prime factors,

$\begin{array}{c}18=2\times 3\times 3\\ 24=2\times 2\times 2\times 3\\ 30=2\times 3\times 5\end{array}$

So,

$LCM(18,24,30)=2\times 2\times 2\times 3\times 3\times 5$

$=360$

Hence, $LCM$ of $18,24,30$ is $360$ by prime factorization.

The smallest six-digit number is $100000$.

$100000÷360=277.78$

This implies that the six-digit number divisible by $18,24,30$ can be given as

$278\times 360=100080$