Find the least common multiple of the following polynomials 9x, 22x, and 3x^2

To find the least common multiple (LCM) of the polynomials 9x, 22x, and 3x², we need to consider both the coefficients and the variables.

First, let’s find the LCM of the coefficients:

• The coefficients are 9, 22, and 3.
• We can find the prime factorization of each number: 9 = 3², 22 = 2 * 11, and 3 = 3¹.

The LCM of these coefficients will take the highest power of each prime factor:

• For 2, the highest power is 2¹ from 22.
• For 3, the highest power is 3² from 9.
• For 11, the highest power is 11¹ from 22.

So the LCM of the coefficients is:

LCM(9, 22, 3) = 2¹ * 3² * 11¹ = 2 * 9 * 11 = 198.

Now, let’s consider the variable part. The polynomials have:

• 9x and 22x have x¹.
• 3x² has x².

The highest power of x here is x².

Therefore, combining both parts, the LCM of the polynomials 9x, 22x, and 3x² is:

LCM(9x, 22x, 3x²) = 198x².

In conclusion, the least common multiple of 9x, 22x, and 3x² is 198x².