Question

Find the greatest 4-digit number exactly divisible by 3, 4 and 5?

Answer 1

Answer

LCM of 3,4,5 = 60

Largest 4 digit number divisible by 60 = 9960

Answer = 9960

Answer 2

The greatest 4-digit number exactly divisible by 3, 4 and 5 is 9960

Given :

The numbers 3 , 4 , 5

To find :

The greatest 4-digit number exactly divisible by 3, 4 and 5

Solution :

Step 1 of 2 :

Find LCM of 3 , 4 , 5

3 is a prime number

4 = 2 × 2

5 is a prime number

LCM of 3 , 4 , 5

= 2 × 2 × 3 × 5

= 60

Step 2 of 2 :

Find the greatest 4-digit number exactly divisible by 3, 4 and 5

The greatest 4 digit number = 9999

If we divide 9999 by 60 we get 166 as quotient and 39 as remainder

Hence the required number

= 9999 - 39

= 9960

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