Question

Find the greatest number of six digits exactly divisible by 24 , 15 and 36 ?

Answer 1

SOLUTION :  

The greatest number of  6 digits  =  999999

First, we need to find the LCM of 24, 15 and 36 and then divide 6 digits number 999999 by the LCM and subtract the remainder  from 6 digit number 999999.

24, 15 and 36

24 = 2 x 2 x2 x3

15 = 3 x 5

36 = 2 x 2 x 3 x 3

L.C.M of 24, 15 and 36 = 360

Now, 999999 /  360

quotient =  2777

Remainder =  279

Therefore, the remainder is 279. Hence the required number is = 999999 – 279 = 999720

Hence, 999720 is the greatest number of 6 digits exactly divisible by 24, 15 and 36.

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Answer 2

We need to find the lcm of 24, 15, 36.

$24 = 2 \times 2 \times 2 \times 3 = {2}^{3} \times 3 \\ \\ 15 = 3 \times 5 \\ \\ 36 = 2 \times 2 \times 3 \times 3 = {2}^{2} \times {3}^{2} \\ \\ so \: lcm = {2}^{3} \times {3}^{2} \times 5 = 360$

So the 6 digit no. Should be multiple of 360.

Now we need to divide the largest 6 digit no. By 360. I. E. 999999

After doing this 279 is left as reminder.

So now subtract 279 from 999999

999999-279=999720.

Answer = 999720.