Question
Find the least $5-$digit number which is exactly divisible by $20, 25, 30.$
✓
Answer
Least five digit number $= 10000$
$\begin{array}{c|c}5&20,25,30\\\hline2&4,5,6\\\hline2&2,5,3\\\hline3&1,5,3\\\hline5&1,5,1\\\hline&1,1,1\end{array}$
$LCM$ of $20, 25, 30$ is $300.$
But we want the least five digit number which is divisible by $20, 25, 30$.
So, we will multiply the $LCM$ by a number that makes it the least five digit number divisible by $20, 25, 30.$
$300 \times 31 = 9300$
$300 \times 32 = 9600$
$300 \times 33 = 9900$
$300 \times 34 = 10200$
So, the least five digit number divisible by $20, 25, 30$ is $10200.$
$\begin{array}{c|c}5&20,25,30\\\hline2&4,5,6\\\hline2&2,5,3\\\hline3&1,5,3\\\hline5&1,5,1\\\hline&1,1,1\end{array}$
$LCM$ of $20, 25, 30$ is $300.$
But we want the least five digit number which is divisible by $20, 25, 30$.
So, we will multiply the $LCM$ by a number that makes it the least five digit number divisible by $20, 25, 30.$
$300 \times 31 = 9300$
$300 \times 32 = 9600$
$300 \times 33 = 9900$
$300 \times 34 = 10200$
So, the least five digit number divisible by $20, 25, 30$ is $10200.$
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