To find the least common multiple (LCM) of the polynomials 5y² and y⁴, we start by identifying the components of each polynomial.
The first polynomial, 5y², can be broken down into its factors as follows:
- 5 (a constant)
- y² (the variable raised to the power of 2)
The second polynomial, y⁴, is simply the variable y raised to the power of 4. Since there is no constant factor in this polynomial, we only focus on the variable component.
Next, we find the LCM by taking the highest power of each factor present in the polynomials.
- For the constant term, the LCM will simply be 5, since it’s the only constant factor present.
- For the variable y, we compare the powers: we have y² from 5y² and y⁴ from y⁴. The highest power is y⁴.
Now we can combine these results to form the LCM:
LCM = 5 * y⁴
Thus, the least common multiple of the polynomials 5y² and y⁴ is 5y⁴.