What is the smallest numbers, greater then $5$ , which when divided by $20, 30$ and $40$ leaves remainder $5$ ?

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Solution

The smallest number greater than $5$ which leaves remainder $0$ when divided by $20, 30, 40$ is LCM of $20, 30, 40$
(Image )
$10 \times 2 \times 3 \times 2 = 120$
$∴$ Number which leaves remainder $5$
$= 120 + 5$
$= 125$
as $125 / 20, 125 / 30, 125 / 40$ leaves remainder $5$

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