Answer :
The greatest number of four digits divisible by 15, 25, 40, and 75 is 9600.
To find the greatest number of four digits which is divisible by 15, 25, 40, and 75, we must find the Least Common Multiple (LCM) of these numbers and identify the largest multiple of this LCM that is still a four-digit number.
First, we need to determine the prime factors of each number:
15 = 3 × 5
25 = 5×5
40 = 2×2×2× 5
75 = 3 × 5×5
The LCM is obtained by taking the product of commom factors and non common factors.
LCM= Common factors × Non-Common factors
LCM= 3×5×5×2×2×2
LCM = 600
The greatest four-digit number divisible by 15, 25, 40, and 75 is the largest multiple of 600 that is less than 10000.
Dividing 10000 by 600 gives:
10000÷600=16 remainder 400
So, the greatest four-digit number that is a multiple of 600 is:
600∗16=9600
Therefore, the greatest number of four digits divisible by 15, 25, 40, and 75 is 9600.
