Gujarat BoardEnglish MediumSTD 6MATHSPlaying with numbers3 Marks
Question
Find the smallest $5$-digit number which is exactly divisible by $20, 25, 30.$
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Answer
$ 20=1 \times 2 \times 2 \times 5=2^2 \times 5^1 $
$ 25=1 \times 5 \times 5 \times 31=5^2 $
$ 30=1 \times 2 \times 3 \times 5=2^1 \times 3^1 \times 5^1$
$LCM$ of $20,25$ and $30=2^2 \times 3^1 \times 5^2=300$
Smallest five digit number is $10000$
Now, if we divide $10000$ by $60$, we will get $33.33$ as quotient.
The integer just greater than $33.33$ is $34$
$\therefore$ Required number $= 300 \times 34 = 10200$
Hence, the smallest $5$-digit number which is exactly divisible by $20, 25, 30$ is $10200.$
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