Question

Find the greatest number of 6 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

Solutions :-


The greatest number of 6 digits = 999999


Find the LCM of 24, 15 and 36 :-

Prime Factors of 24, 15 and 36 are
24 = 2 × 2 × 2 × 3 = 2³ × 3
15 = 3 × 5
36 = 2 × 2 × 3 × 3 = 2² × 3²

LCM of 24, 15 and 36 = 2³ × 3² × 5 = 360


Now,
Divide 999999 by 360 :-

After division we get,

Quotient = 2777
Remainder = 279



To find the greatest six digits number exactly divisible by 24, 15 and 36. We have to subtract 279 from 999999.

Therefore,
999999 - 279 = 999720



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