To find the least common multiple (LCM) of the two expressions
-
Factorizing the constants:
-
Identifying the variable parts:
- The variable part for the first expression is
. - The variable part for the second expression is
.
- The variable part for the first expression is
-
Finding the LCM of the constants:
- The LCM of the constants
and can be found by taking the highest power of each prime factor:- For
, the maximum power is (from ). - For
, the maximum power is (from both).
- For
- Thus, the LCM of the constants is:
- The LCM of the constants
-
Finding the LCM of the variable parts:
- The LCM of the variable parts
and is determined by taking the highest power:- The maximum power of
is .
- The maximum power of
- Therefore, the LCM of the variable parts is:
- The LCM of the variable parts
-
Combining the results:
- The overall LCM is the product of the LCM of the constants and the LCM of the variable parts:
- The overall LCM is the product of the LCM of the constants and the LCM of the variable parts:
Thus, the least common multiple