How do you find an LCM with variables?

Answer 1

By attacking them separately.

Example 30x2y3z4 and 42x4y5z2

Factor the coefficients.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210

For variables, just choose the highest number exponent.

The LCM of the above example is 210x4y5z4

Answer 2

Choose the variable with the highest exponent. The LCM of x^2y^4 and x^5y^3 is x^5y^4

Answer 3

Factor the coefficients normally. Choose the higher powers of the variables.

Answer 4

Example: 3x4y2 and 9x3y5

Treat the whole numbers normally. The LCM of 3 and 9 is 9. Choose the highest value of the variables. In this case, the LCM is 9x4y5

Answer 5

You take each variable, in turn along with its highest power in any of the terms.

Thus LCM(x^2*y*z^3, x^4*y^2, y^2*z^2) = x^4*y^2*z^3.