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The least common multiple (LCM) of two whole numbers a and b is the smallest whole number that is a multiple of both a and b. It is denoted as LCM(a,b). The least common multiple of a and b is the smallest whole number that is divisible by both a and b.
Polynomials can also have a least common multiple. The LCM of two or more polynomials is the smallest multiple of both polynomials. In other words, the LCM is the smallest expression that can be evenly divided by each of the given polynomials.
| Polynomials | Factor | LCM | Explanation |
|---|---|---|---|
| 4x^3 and 6xy^2 | 2^2 * x^3 and 2* 3 * x * y^2 | 12x^3y^2 | 12x^3y^2 is the smallest expression that is divisible by both 4x^3 and 6xy^2. |
| 3x^3+3x^2 and x^2+5x+4 | 3 * x^2 * (x+1) and (x+1)(x+4) | 3x^2(x+1)(x+4) | 3x^2(x+1)(x+4) is the smallest expression that is divisible by both 3x^3+3x^2 and x^2+5x+4. |
Finding the LCM of polynomials requires identifying the factors with the highest power that appear in each polynomial.