Question
Find the least 5-digit number which is exactly divisible by 20, 25 and 30.
✓
Answer
$\quad 20=1 \times 2 \times 2 \times 5=2^2 \times 5^1$
$25=1 \times 5 \times 5 \times 31=5^2$
$30=1 \times 2 \times 3 \times 5=2^1 \times 3^1 \times 5^1$
LCM of 20,25 and $30=2^2 \times 3^1 \times 5^2=300$
Least 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 least 5-digit number which is exactly divisible by $20,25,30$ is 10200.
$25=1 \times 5 \times 5 \times 31=5^2$
$30=1 \times 2 \times 3 \times 5=2^1 \times 3^1 \times 5^1$
LCM of 20,25 and $30=2^2 \times 3^1 \times 5^2=300$
Least 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 least 5-digit number which is exactly divisible by $20,25,30$ is 10200.
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