Find the greatest number of 6 digits exactly divisible by 24,
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 

$24=2^{3} \times 3$

$15=3 \times 5$

$36=2^{2} \times 3^{2}$

L.C.M of 24,15 and $36=360$

Since $\frac{999999}{360}=2777 \times 360+279$

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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