Question

find the greatest number of 3 digit that can be exactly divided by 25 45 and 60

Answer 1

Find LCM of 25, 45, and 60:

25 = 5²

45 = 5 x 3²

60 = 5 x 3 x 2²

LCM = 5² x 3² x 2² = 900

Find Greatest 3-digit number divisible by these numbers:

999 ÷ 900 =1.11

 900 x 1 = 900

Answer: The number is 900

Answer 2

First find the LC.M. of 25,45 and 60.
5 |25,45,60
3 |5,9,12
3 |5,3,4
5 |5,1,4
2 |1,1,4
2 |1,1,2
|1,1,1. Least Common Multiple of these three numbers =5×3×3×5×2×2=900.So the greatest number of 3 digits which can be exactly divided by 25,45,60 is 900 only. Hope it helps you