How do you find the Least common multiple of #20x^3, 16x^4#?

Question

Benjamin Altschul · Accepted Answer

#80x^4# #20x^3, 16x^4# #4x^3 [5 , 4x]# LCM = #4x^3xx5xx4x# = #80x^4#

Aurora Arias · Answer

undefined To find the least common multiple (LCM) of $20x^3$ and $16x^4$, follow these steps:

1. Factor each term into its prime factors.
2. Identify the highest power of each prime factor that appears in either expression.
3. Multiply these highest powers together to find the LCM.

For $20x^3$:
- Factor 20 into its prime factors: $20 = 2^2 \times 5$.
- There's only one term of $x^3$, so the highest power of $x$ is $x^3$.

For $16x^4$:
- Factor 16 into its prime factors: $16 = 2^4$.
- There's only one term of $x^4$, so the highest power of $x$ is $x^4$.

Now, to find the LCM:
- For the prime factor 2, the highest power is 4 (from $16x^4$).
- For the prime factor 5, it's only present in $20x^3$, so its power is 0.
- For the variable $x$, the highest power is 4 (from $16x^4$).

Multiply these highest powers together:
$$ LCM = 2^4 \times 5^0 \times x^4 = 16x^4 $$

Therefore, the least common multiple of $20x^3$ and $16x^4$ is $16x^4$.

Nova Allen · Answer

undefined To find the least common multiple (LCM) of $ 20x^3 $ and $ 16x^4 $, first, factor each term into its prime factors. Then, take the highest power of each prime factor that appears in either number, and multiply these powers together to get the LCM.

For $ 20x^3 $, the prime factorization is $ 2^2 \times 5 \times x^3 $.

For $ 16x^4 $, the prime factorization is $ 2^4 \times x^4 $.

Next, take the highest power of each prime factor that appears in either number:

- The highest power of 2 is $ 2^4 $.
- The highest power of 5 is $ 5^1 $.
- The highest power of $ x $ is $ x^4 $.

Multiply these together to find the LCM:

$ LCM = 2^4 \times 5^1 \times x^4 $

Simplifying this expression gives:

$ LCM = 16 \times 5 \times x^4 $

Which further simplifies to:

$ LCM = 80x^4 $

So, the least common multiple of $ 20x^3 $ and $ 16x^4 $ is $ 80x^4 $.