The greatest 6-digit number divisible by 24, 15, and 36 is 999720.
To find this, we need to determine the least common multiple (LCM) of the given numbers, then find the largest 6-digit number divisible by that LCM. Let's break this down:
Finding the LCM
First, we need to find the prime factorization of each number:
- 24 = 23 * 3
- 15 = 3 * 5
- 36 = 22 * 32
The LCM is found by taking the highest power of each prime factor present in the numbers:
LCM (24, 15, 36) = 23 32 5 = 8 9 5 = 360.
So, we need to find the largest 6-digit number divisible by 360.
Finding the Largest 6-digit Number Divisible by the LCM
The largest 6-digit number is 999,999. Now we need to divide this by 360 to see how many times it goes in completely:
999,999 / 360 = 2777.775
This means that 360 goes into 999,999 about 2777 times completely. So let's find that whole number:
2777 * 360 = 999720
This result, 999,720, is the largest 6-digit number divisible by 360 which is the LCM of 24, 15 and 36.
Final Answer
Therefore, the greatest 6-digit number divisible by 24, 15, and 36 is 999720, which is consistent with the provided reference:
∴ 999720 is the greatest number 6-digit number divisible by 24,15 and 36.
