Question
Find the least common multiple (LCM) of 16xy^3 and 20x^3y^2
Answer
4.6
(255 Votes)
Callum
Professional · Tutor for 6 years
Answer
The least common multiple (LCM) of
and
is
.
Explanation
## Step 1: First, we need to find the prime factorization of each term. ## Step 2: The prime factorization of 16 is
, of
is
, and of
is
. So, the prime factorization of
is
.## Step 3: The prime factorization of 20 is
, of
is
, and of
is
. So, the prime factorization of
is
.## Step 4: To find the least common multiple (LCM), we take the highest power of each prime factor that appears in either factorization. ### The formula for LCM is: ### \(LCM = 2^{max(4,2)} \times 5^{max(0,1)} \times x^{max(1,3)} \times y^{max(3,2)}\)## Step 5: Substitute the values into the formula to get the LCM.