Question:
Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.
Solution:
Prime factorization:
15 = 3 × 5
$24=2^{3} \times 3$
$36=2^{2} \times 3^{2}$
LCM = product of greatest power of each prime factor involved in the numbers $=2^{3} \times 3^{2} \times 5=360$
Now, the greatest four digit number is 9999.
On dividing 9999 by 360 we get 279 as remainder.
Thus, 9999 − 279 = 9720 is exactly divisible by 360.
Hence, the greatest number of four digits which is exactly divisible by 15, 24 and 36 is 9720.