Answer :
Step-by-step explanation:
To find the smallest number of 6 digits that is divisible by 24, 15, and 36, we need to find the least common multiple (LCM) of these three numbers.
The prime factorization of 24 is 2^3 * 3, the prime factorization of 15 is 3 * 5, and the prime factorization of 36 is 2^2 * 3^2.
To find the LCM, we take the highest power of each prime factor that appears in any of the numbers. Therefore, the LCM will be 2^3 * 3^2 * 5 = 360.
Now, we need to find the smallest 6-digit number divisible by 360. The largest 6-digit number is 999,999.
To find the smallest multiple of 360 that is greater than or equal to 100,000, we divide 100,000 by 360 and round up to the nearest whole number.
100,000 divided by 360 is approximately 277.78, so we round up to 278.
To find the smallest 6-digit number divisible by 360, we multiply 360 by 278.
360 * 278 = 100,080.
Therefore, the smallest number of 6 digits exactly divisible by 24, 15, and 36 is 100,080.