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Which is the smallest 4-digit number divisible by 8, 10 and 12?
Given:
8, 10 and 12
To find:
We have to find the smallest 4-digit number divisible by 8, 10 and 12
Solution:
To find the smallest 4 digit number which is exactly divisible by 8, 10 and 12, we have to first find the LCM of 8, 10 and 12:
$8\ =\ 2\ \times \ 2\ \times \ 2$
$10\ =\ 2\ \times \ 5$
$12\ =\ 2\ \times \ 2\ \times \ 3$
LCM = 2 $\times $ 2 $\times $ 2 $\times $ 3 $\times $ 5 = 120
So, LCM of 8, 10 and 12 is 120. But we want the least 4 digit number, which is exactly divisible by 8, 10 and 12.
Smallest 4 digit number = 1000.
Now,
$1000\ =\ ( 8\ \times \ 120) \ +\ 40$
Next higher quotient is 9.
So, the required number = 9 × 120 = 1080
Hence, the required number is 1080, which is exactly divisible by 8, 10 and 12.
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