Find the lowest common multiple of the following.
21=3x7
33=3x11
20=2squared x 5
To find the lowest common multiple (LCM) of the numbers given, you look at each of the prime factors that you need to cover all of the numbers.
The provided factorization for each number:
- 21 = 3 x 7
- 33 = 3 x 11
- 20 = 2^2 x 5
We take the highest powers of each prime factor that appear in the factorization of any of the numbers.
- For the prime number 2, the highest power is 2^2 (from 20).
- For the prime number 3, the highest power is 3^1 (which appears in both 21 and 33).
- For the prime number 5, the highest power is 5^1 (from 20).
- For the prime number 7, the highest power is 7^1 (from 21).
- For the prime number 11, the highest power is 11^1 (from 33).
The LCM is then found by multiplying these highest powers together:
LCM = 2^2 x 3^1 x 5^1 x 7^1 x 11^1
LCM = 4 x 3 x 5 x 7 x 11
LCM = 12 x 35 x 11
LCM = 420 x 11
LCM = 4620
So, the lowest common multiple of 21, 33, and 20 is 4620.