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Question
Find the greatest number of 6 digits exactly divisible by 24, 15 and 36.
Solution
TO FIND: Greatest number of 6 digits exactly divisible by 24, 15 and 36
The greatest 6 digit number be 999999
24, 15 and 36
`24=2^2xx3`
`15=3xx5`
`36=2^2xx3^2`
L.C.M of 24,15 and 36 = 360
Since `99999/360 =2777xx360+279`
Therefore, the remainder is 279.
Hence the desired number is equal to
`=999999-279`
= 999720
Hence 999720 is the greatest number of 6 digits exactly divisible by 24, 15 and 36.
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