Question

Find the least number of five digits which is exactly divisible by 32,36 and 45 (with full solution)

Answer 1

First take out the LCM of 32,36 and 45.
LCM=1440
Smallest 5 digit number=10000
Divide 10000 by 1440
Remainder is 1360
Req. no.=10000+(1440-1360)
              =10000+80
              =10080
Ans.=10080 is the least no. of 5 digits which is exactly divisible by 32,36 and 45.

Answer 2

Answer:

The required number is 10080 which is exactly divisible by 32,36 and 45.

Step-by-step explanation:

Given : The least number of five digits which is exactly divisible by 32,36 and 45.

To find : The least number ?

Solution :

The least 5-digit number is 10000.

Now, we find the LCM of 32,36 and 45.

2 | 32  36  45

2 | 16   18  45

2 |  8    9   45

2 |  4    9   45

2 |  2    9   45

3 |  1    9    45

3 |  1    3     15

5 |  1    1      5

  |  1    1      1

$LCM(32,36,45)=2\times 2\times 2\times 2\times 2\times 3\times 3\times 5$

$LCM(32,36,45)=1440$

Divide 10000 by 1440 so that we get the remainder,

$10000 = 6\times 1440 + 1360$

Remainder is 1360.

The required number is

$=10000+(1440-1360)$

$=10000+80$

$=10080$

Therefore, The required number is 10080 which is exactly divisible by 32,36 and 45.