How do you find the Least common multiple of #18xy^2, 15y^3#?

Question

Jeremiah Andrews · Accepted Answer

The LCM is #3y^2#

Find the prime factorization (a composite number divided into prime numbers multiplied together) before attempting to find the LCM.

#18xy^2=3*3*2*x*y*y#

#15y^3=3*5*y*y*y#

They all have at least one 3 and two y's, so now circle the ones that they have in common. Multiply these totals to find your LCM.

Roman Alvarez · Answer

undefined To find the least common multiple (LCM) of $18xy^2$ and $15y^3$, first factorize each expression:

$18xy^2 = 2 \times 3 \times 3 \times x \times y \times y$

$15y^3 = 3 \times 5 \times y \times y \times y$

Next, identify the highest power of each prime factor that appears in either expression:

- The highest power of 2 in $18xy^2$ is $2^1$.
- The highest power of 3 in $18xy^2$ is $3^2$.
- The highest power of 5 in $18xy^2$ is $5^0$.
- The highest power of $x$ in $18xy^2$ is $x^1$.
- The highest power of $y$ in $18xy^2$ is $y^2$.

- The highest power of 2 in $15y^3$ is $2^0$.
- The highest power of 3 in $15y^3$ is $3^1$.
- The highest power of 5 in $15y^3$ is $5^1$.
- The highest power of $x$ in $15y^3$ is $x^0$.
- The highest power of $y$ in $15y^3$ is $y^3$.

Now, combine the highest powers of each prime factor to find the LCM:

LCM = $2^1 \times 3^2 \times 5^1 \times x^1 \times y^3$

LCM = $6xy^3$