Question

what is the largest four digit number that is divisible by each of 15'25'and35

Answer 1

Answer:

Step-by-step explanation:

Given numbers are 15, 25 and 35.

In order to find largest four digit number that is divisible by all of them lets first find LCM of all these numbers.

To find LCM lets write all of them in prime factor form

15 = 3 x 5

25 = 5 x 5

35 = 7 x 5

LCM = 3 x 5 x 5 x 7 = 525

Now any number that is divisible by 525 is also divisible by 15, 25 and 35.

As we know our highest four digit number is 9999, so if we divide 9999 by 525, we get the remainder 24. Now if we subtract 24 from 9999 we get 9975. This is our highest four digit number which is divisible by 15, 25 and 35.

Check

$\frac{9975}{15} = 665$

$\frac{9975}{25} = 399$

$\frac{9975}{35} = 285$

Answer 2

Answer:

9975

Step-by-step explanation:

Given to find the largest four digit number that is divisible by each of 15' 25' and 35.

First, we need to find the LCM of 15,25 and 35. We get the factors as 5 x 3 x 5 x 7 = 525

Now the largest four digit number is 9999. Divide 9999 / 525, we get 24 as remainder.

Subtract 9999 - 24 = 9975

Now the largest four digit number which is divisible by 15, 25 and 35 is 9975