How many integers between 1000 and 2000 have all three of the numbers 15,20 and 25 as factors

3

Step-by-step explanation:

We have that,

Least common multiple of the numbers 15, 20 and 25 is 300.

So, any number being factor of 300 will also be a factor of all three numbers 15, 20 and 25.

Now, the factors of 300 in the range 1000 and 2000 are 1200, 1500 and 1800.

So, the numbers 1200, 1500 and 1800 will have the numbers 15, 20 and 25 as factors.

Hence, there are three numbers having 15, 20 and 25 as factors.