Find the lowest common multiple of the following.
25=3x5
25=5 squared
30=2x3x5
To find the lowest common multiple (LCM) of the numbers given, we need to combine the prime factors at their highest power used in any of the numbers.
Let's write down the prime factorization of each number:
- The first expression you provided, "25 = 3x5," seems to be incorrect, as 25 is not divisible by 3. The correct prime factorization of 25 is 5^2 (5 squared).
- The second expression, "25 = 5 squared," is correct.
- The third expression, "30 = 2x3x5," is correct and represents the prime factorization of 30.
So the prime factorization of each number is:
- 25 = 5^2
- 30 = 2 x 3 x 5
The LCM of these numbers would involve the highest power of each prime number that appears in any of the factorizations.
- The highest power of 2 present in the factorizations is 2^1 (from 30).
- The highest power of 3 present is 3^1 (from 30).
- The highest power of 5 present is 5^2 (from 25).
Now we multiply these highest powers together to get the LCM:
LCM = 2^1 x 3^1 x 5^2
LCM = 2 x 3 x 25
LCM = 6 x 25
LCM = 150
So the lowest common multiple of 25 and 30 is 150.