Question

Find the greatest number of 5 digits which is exactly divisible by 20,24,35 & 45

Answer 1

First of all we will find the L.C.M of 20, 24, 35 45.
So, L.C.M= 2×2×5×3×2×7×3 = 1520.
Greatest 5 digit number= 99999.
We will divide 99999 by 1520 and find the remainder.

99999÷ 1520=
Q= 65
R= 1199.

A.T.Q we need a greatest 5 digit no. exactly divisible by 1520.

Therefore, the required number is 99999-1199=9800.

Answer 2

Answer:

The required number is 98280 which is exactly divisible by 20,24,35 & 45.

Step-by-step explanation:

To find : The Greatest 5 digit number exactly divisible by 20,24,35 & 45?

Solution :  

The greatest 5-digit number is 99999.

We find the LCM of 20,24,35 & 45.

2 | 20  24  35  45

2 | 10   12  35  45

2 |  5   6   35  45

3 |  5   3   35  45

3 |  5   1   35   15

5 |  5   1   35   5

7  |  1   1    7     1

  |  1   1    1     1

$LCM(20,24,35,45)=2\times 2\times 2\times 3\times 3\times 5\times 7$

$LCM(20,24,35,45)=2520$

Divide 99999 by 2520 so that we get the remainder,

$99999 = 39 \times 2520 + 1719$

Remainder is 1719.

Now, Subtract the remainder from 99999.

$99999-1719=98280$

Therefore, The required number is 98280 which is exactly divisible by 20,24,35 & 45.