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Find the number closest to 10000 and divisible by 30 , 45 , 15.
Given numbers are 30, 45, 15.
To do:
We have to find the number closest to 10000 which is exactly divisible by 30 , 45 and 15.
Solution:
The number divisible by 30 , 45 , 15 is a multiple of their LCM.
Multiples of 30 - 30 , 60 , 90 , 120 ...
Multiples of 45 - 45 , 90 , 135 , 180...
Multiples of 15 - 15 , 30 , 45 , 60 , 75 , 90 , 105 , 120....
So, the Least Common Multiple of 30 , 45 , 15 is 90.
Now, the number closest to 10000 which is a multiple of 90 is,
Divide 10000 by 90.
111
______________
90 ) 10000
90
_________________
100
90
_________________
100
90
_________________
10
The remainder is 10.
$10000 - 10 = 9990$
So, 9990 is the number closest to 10000 and divisible by 30 , 45 and 15.
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