Question

find the greatest number of 6 digits exactly divisible by 24,15,and36

Answer 1

Theory:

we know that the LCM of these number (i.e, LCM of 24, 15, 36) exactly divisible by each.

so, if LCM of these number divide the required number exactly, it means the number is exactly divisible by each of these numbers.

step 1: find the LCM of 24, 15, 36.
LCM of ( 24, 15, 36) = 360.

step2: Find the Greatest Number of 6 Digit which is nothing but 999999

step3: Divide 999999 by 360. we will get 279 as remainder.

step4: Subtract the remainder from original number. i.e, ( 999999 - 279 ) = 999720

Now 999720 is exactly divisible by 360. (LCM of those given number)

Now we will check divisibility by each of those given number.

999720/4 = 41655
999720/15 = 66648
999720/36 = 27770

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

Hope it helps!