Question

Find the greatest number of 6 digits numbers exactly divisible by 24, 15 and 36.

Answer 1

Hint: In order to solve this problem you need to find the LCM of the numbers and divide it to check if it leaves a remainder. If it then subtract that remainder from the greatest number you will get your answer.

Complete step-by-step solution:
We know that if a number is divisible by 24,15 and 36 then the number should be divisible by a common multiple of 24,15 and 36 so, we will find out the LCM of 24,15 & 36 is 360.

Now greatest 6 digit number is 999999.

Now by doing $\dfrac{{999999}}{{360}}$​ we will get a reminder 279.

So, the six digit number which will exactly divided by 24, 15, 36 can be calculated as:-
999999−279 = 999720

999720 is the greatest 6 digit number divisible by 24, 15 and 36.

Hence, the answer is 999720.

Note: In this problem we have taken the LCM because it will give the lowest common factor of 24, 15 and 36 so dividing it by that will be the same as dividing by all the three numbers. Then we found the remainder is left; it means the number is not fully divisible so we subtracted the 6 digits number with the remainder so that the number is fully divisible.