Find the greatest number consisting of 6 digits which is exactly divisible by 24,15,36.
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SOLUTION :
The greatest number of 6 digits = 999999
First, we need to find the LCM of 24, 15 and 36 and then divide 6 digits number 999999 by the LCM and subtract the remainder from 6 digit number 999999.
24, 15 and 36
24 = 2 x 2 x2 x3
15 = 3 x 5
36 = 2 x 2 x 3 x 3
L.C.M of 24, 15 and 36 = 360
Now, 999999 / 360
quotient = 2777
Remainder = 279
Therefore, the remainder is 279. Hence the required number is = 999999 – 279 = 999720
Hence, 999720 is the greatest number of 6 digits exactly divisible by 24, 15 and 36.
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