What is the Lowest common multiple of 10500 and 38808

Step 1: Find the prime factorizations of the numbers:

- For 10500:

10500=2^2\cdot3^1\cdot5^3\cdot7^1

- For 38808:

38808=2^3\times3^2\times7^2\times11^1

Step 2: Determine the LCM by taking the highest power of each prime factor that appears in any of the factorizations:

- For prime 2: highest power is 2^3

- For prime 3: highest power is 3^4

- For prime 5: highest power is 5^4

- For prime 7: highest power is 7

- For prime 11: highest power is 11

Step 3: Multiply these together to get the LCM:

\text{LCM}=2^3\times3^2\times5^3\times7^2\times11^1

Step 4: Calculate the value:

2^3=8,\quad3^2=9,\quad5^3=125,\quad7^2=49,\quad11^1=11

\text{LCM}=8\times9\times125\times49\times11=4851000