Find the lowest common multiple of the following
280 = 2 power 3x5x7
6600=2 power of 3x3x5 squared x11
Let's write down the prime factorization of each number clearly:
280 = 2^3 * 5 * 7
6600 = 2^3 * 3^2 * 5^2 * 11
To find the lowest common multiple (LCM) of these two numbers, you want to take the highest powers of all the prime factors that appear in either number.
So the LCM will have the following factors:
- The highest power of 2 that appears in either number is 2^3.
- The highest power of 3 that appears is 3^2 (from 6600, since 280 doesn't have a factor of 3).
- The highest power of 5 that appears is 5^2 (from 6600, even though 280 only has 5^1).
- The highest power of 7 that appears is 7^1 (from 280, since 6600 doesn't have a factor of 7).
- The highest power of 11 that appears is 11^1 (from 6600, since 280 doesn't have a factor of 11).
Therefore, the LCM of 280 and 6600 is:
2^3 * 3^2 * 5^2 * 7 * 11.
Calculating this gives:
8 * 9 * 25 * 7 * 11
= 72 * 25 * 7 * 11
= 1800 * 7 * 11
= 12600 * 11
= 138600
Therefore, the lowest common multiple of 280 and 6600 is 138600.