Question

Largest 4 digit number exacty divisible by 30 and 40

Answer 1

Let the 4 digit number be x

The largest 4 digit number is 9999

We have asked a number which is divisible by 30 and 40

So,
First we have to find the lcm of 30 and 40

Lcm means least common multiple
So,
Prime factorization of the two numbers is :-

30 = 2*3*5
40= 2*2*2*5

Common numbers is 2 , 5
So,
LCM = 2*5*2*2*3 = 120

Now,

We have to divide the largest 4 digit number with 120
So,

Dividing the numbers

9999/120

So, the quotient is 83
Remainder is 39

So,
We have to subtract the remainder from the largets 4 digit number that is 9999

So,
The number is 9999 - 39 = 9960

So,
The largest 4 digit number divisible by both 30 and 40 is 9960