Find the lowest common multiple of the following
100=2 squaredx5 squared
150=2x3x5 squared
To find the lowest common multiple (LCM) of 100 and 150, we need to combine the prime factors at their highest powers that appear in the factorization of both numbers.
From your input:
100 = 2^2 x 5^2
150 = 2 x 3 x 5^2
The LCM will take the highest power of each prime that appears:
- For the prime number 2, the highest power in both numbers is 2^2 (present in 100).
- For the prime number 3, the highest power is 3^1 (present in 150, since 100 does not have any factor of 3).
- For the prime number 5, the highest power is 5^2 (present in both 100 and 150).
Multiply these together to get the LCM:
LCM = 2^2 x 3^1 x 5^2
LCM = 4 x 3 x 25
LCM = 12 x 25
LCM = 300
So, the lowest common multiple of 100 and 150 is 300.