Find the lowest common multiple of the following
30=2x3x5
80=2 power of 4x5
120=2 power of 3x3x5=
To find the lowest common multiple (LCM) among several numbers, you can do this by finding the highest powers of all the prime factors that occur in any of the numbers and then multiplying these highest powers together.
Given the prime factorizations:
30 = 2 x 3 x 5
80 = 2^4 x 5
120 = 2^3 x 3 x 5
First, list all the prime factors that appear in any of the numbers and find the highest power for each prime factor that appears in any of the factorizations:
The prime factors are 2, 3, and 5.
Highest powers for each prime factor:
- For 2, the highest power is 2^4 (from 80).
- For 3, the highest power is 3^1 (from 30 and 120).
- For 5, the highest power is 5^1 (from all three numbers).
Now, multiply the highest powers of the prime factors:
LCM = 2^4 x 3^1 x 5^1
LCM = 16 x 3 x 5
LCM = 48 x 5
LCM = 240
Therefore, the lowest common multiple of 30, 80, and 120 is 240.