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 .