Question

find the least common multiple of these two expressions.
$6w^{6}y^{2}x^{3}$ and $10w^{7}x^{5}$

Explanation:

Step1: Factor the coefficients

Factor 6 and 10. \(6 = 2\times3\), \(10 = 2\times5\). The LCM of 6 and 10 is \(2\times3\times5 = 30\).

Step2: Find LCM of variables with \(w\)

For \(w\), the exponents are 6 and 7. LCM takes the higher exponent, so \(w^7\).

Step3: Find LCM of variables with \(y\)

Only the first expression has \(y\) with exponent 2, so \(y^2\).

Step4: Find LCM of variables with \(x\)

Exponents of \(x\) are 3 and 5. Take the higher exponent, so \(x^5\).

Step5: Combine all parts

Multiply the LCM of coefficients and LCM of each variable: \(30\times w^7\times y^2\times x^5 = 30w^7y^2x^5\).

Answer:

\(30w^{7}y^{2}x^{5}\)