Question

find the gretest number of five digits which is exactily divisible by 20,25,28,35,40.​

Answer 1

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 7LCM(20,24,35,45)=2×2×2×3×3×5×7

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

Divide 99999 by 2520 so that we get the remainder,

99999 = 39 \times 2520 + 171999999=39×2520+1719

Remainder is 1719.

Now, Subtract the remainder from 99999.

99999-1719=9828099999−1719=98280

Therefore, The required number is 98280 which is exactly divisible by 20,24,28,35and40