A number is divisible by $24, 25, 120$ if increased by $20$ . Find the number.

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Solution

Step 1: Find the LCM:
Let $x$ be the number.
Then $x + 20$ divisible by $24, 25, 120 .$
LCM of $24, 25, 120 .$
$24 = 2 \times 2 \times 2 \times 3$
$25 = 5 \times 5$
$120 = 2 \times 2 \times 3 \times 2 \times 5$
LCM $= 2 \times 2 \times 2 \times 3 \times 5 \times 5$
LCM $= 600$
Step 2: Find the number:
So the number $x$ will be $600 - 20 = 580$
Hence, $580$ is the number.

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