How do you find the Least common multiple of #23u^2, 14v^2#?

Question

Levi Adams · Accepted Answer

The LCM is the product of the two terms, as they have no factor in common.

Put the terms in the form of a prime factor product. The LCM is the product of the highest exponent common and non-common factors, each taken once. #23u^2# is already factorized as #23# is prime. #14v^2 =2*7*v^2# There are no common factors so the LCM is just the product of all factors: #LCM=322u^2v^2#

Skylar Adams · Answer

undefined To find the least common multiple (LCM) of $ 23u^2 $ and $ 14v^2 $, you first factorize each expression. Then, identify the highest power of each prime factor in both expressions. Finally, multiply those prime factors together, including the highest powers.

The prime factorization of $ 23u^2 $ is $ 23 \times u^2 $, and the prime factorization of $ 14v^2 $ is $ 2 \times 7 \times v^2 $.

The highest power of $ 23 $ is $ 23 $, the highest power of $ 2 $ is $ 2 $, the highest power of $ 7 $ is $ 7 $, the highest power of $ u $ is $ u^2 $, and the highest power of $ v $ is $ v^2 $.

Therefore, the least common multiple of $ 23u^2 $ and $ 14v^2 $ is $ 2 \times 7 \times 23 \times u^2 \times v^2 $, which simplifies to $ 322u^2v^2 $.

Roman Alvarez · Answer

undefined To find the least common multiple (LCM) of $23u^2$ and $14v^2$, we need to factor both expressions completely and then identify the highest power of each unique factor that appears in either expression.

The prime factorization of $23u^2$ is $23 \times u \times u$, and the prime factorization of $14v^2$ is $2 \times 7 \times v \times v$.

The LCM will include all the unique factors with their highest powers:

- The unique prime factors are $2$, $7$, $23$, $u$, and $v$.
- The highest power of $2$ is $2^1$.
- The highest power of $7$ is $7^1$.
- The highest power of $23$ is $23^1$.
- The highest power of $u$ is $u^2$.
- The highest power of $v$ is $v^2$.

Therefore, the LCM of $23u^2$ and $14v^2$ is $2 \times 7 \times 23 \times u^2 \times v^2$, which simplifies to $322u^2v^2$.