Question

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Answer 1

Prime factorization:
15 = 3 × 5
24 = 2³ × 3
36 = 2² × 3² 
LCM = product of greatest power of each prime factor involved in the numbers = 2³ × 3² × 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.