Find the lowest common multiple of the following
25=5 squared
20=2 squared x 5
To find the lowest common multiple (LCM) of two numbers, you first need to express each number as a product of its prime factors, which you've already done. Then, for each distinct prime factor that appears in the factorizations, you take the highest power of that factor that appears in either number and multiply all these together.
You've provided the factorizations as:
25 = 5^2 (this means 5 squared or 5 to the power of 2)
20 = 2^2 x 5 (2 squared times 5)
So let's identify the distinct prime factors and their highest powers:
- The prime factors for 25 are just 5 with the highest power being 5^2.
- The prime factors for 20 are 2 (with a highest power of 2^2) and 5 (with a highest power of 5^1).
For the LCM, you take the highest power of each distinct prime factor. Hence, you use 2^2 for the prime factor 2, and 5^2 for the prime factor 5.
So the LCM of 25 and 20 is:
LCM = 2^2 x 5^2
LCM = 4 x 25
LCM = 100
The lowest common multiple of 25 and 20 is 100.