Question

Find the greatest number of 5 digits exactly divisible by 12,15,36

Answer 1

First we will find the LCM of 12,15 and 36

By prime Factorisation,

12=2*2*3

15=5*3

36=2*2*3*3

Now, LCM= 22*32*5

We will find that the LCM is 180

Now, Largest 5 digit number= 99999

Dividing this number by LCM, we get,

99999/180=555.5

Now we will multiply 180 by 555

We will get 99900

We will check now and observe,

99900/12=8325

99900/15=6660

99900/36=2775

Hence 99900 is the greatest 5 digit number divisible by 12,15 and 36.

Answer 2

To find:

"5 digit number" which is divisible by 12, 15 and 36.

Answer:        

First find the LCM (12, 15, & 36)

$12 = 2^{2} \times 3$

$15 = 3 \times 5$

$36 = 2^{2} \times 3^{2}$

LCM $(12, 15, & 36) =2^{2} \times 3^{2} \times 5=180$

99999 is the biggest five digit number

We can find the remainder when 99999 is divided by 180

Thus $99999 = 555 \times 180 + 99$

Therefore, 99 is the remainder when 99999 is divided by 1870

Subtract the remainder 99 from 99999 will get the 99900

Hence, 99900 is the answer.