LCM of 2t, (t-2) and t(t-2)
The factors are:
2, t and (t-2), so the LCM is....
To find the least common multiple (LCM) of three expressions, we first need to factorize each expression and then identify the highest power of each factor.
Let's factorize the given expressions:
Expression 1: 2t
Expression 2: (t - 2)
Expression 3: t(t - 2)
Now, let's determine the highest power of each factor present in any expression:
Factors: 2, t, (t - 2)
Expression 1: 2t has one factor of 2 and one factor of t.
Expression 2: (t - 2) has one factor of (t - 2).
Expression 3: t(t - 2) has one factor of t and one factor of (t - 2).
To calculate the LCM, we take the highest power of each factor:
Factors: 2, t, (t - 2)
Highest power of 2: 1 (from Expression 1)
Highest power of t: 1 (from Expression 1 or Expression 3)
Highest power of (t - 2): 1 (from Expression 2 or Expression 3)
Therefore, the LCM of 2t, (t - 2), and t(t - 2) is: 2 * t * (t - 2) = 2t(t - 2)