Question

The greatest number of five digits which is divisible by 32, 36, 40, 42 and 48 is

Answer 1

first of all we take out the LCM of 32 36 40 42 and 48 and we get the LCM 10080 which is divisible by 32 36 40 42 and 48

Answer 2

Answer:

The required number is 90720 which is exactly divisible  by 32, 36, 40, 42 and 48.

Step-by-step explanation:

To find : The greatest number of five digits which is divisible by 32, 36, 40, 42 and 48?

Solution :  

The greatest 5-digit number is 99999.

Now, Find the LCM of 32,36,40,42 and 48.

2 | 32  36  40  42  48

2 | 16   18   20  21  24

2 | 8     9    10   21  12

2 | 4     9    5    21   6

2 | 2     9    5    21   3

3 | 1      9    5    21   3

3 | 1      3    5     7    1

5 | 1      1     5     7    1

7  | 1      1     1      7    1

   | 1      1     1      1    1

$LCM(32,36,40,42,48)=2\times 2\times 2\times 2\times 2\times 3\times 3\times 5\times 7$

$LCM(32,36,40,42,48)=10080$

Divide 99999 by 10080 so that we get the remainder,

$99999 = 10080 \times9+ 9279$

Remainder is 9279.

Now, Subtract the remainder from 99999.

$99999-9279=90720$

Therefore, The required number is 90720 which is exactly divisible  by 32, 36, 40, 42 and 48.