Question

Find the LCM of the following: $(x+4{)}^2(x-3{)}^3,(x-1)(x+4)(x-3{)}^2$

• A. $(x+4{)}^2(x-3{)}^3(x-1)$
• B. $(x+4{)}^2(x+3{)}^3(x-1)$
• C. $(x-4{)}^2(x-3{)}^3(x-1)$
• D. None of these

Answer 1

The correct option is A $(x+4{)}^2(x-3{)}^3(x-1)$

We know that the least common multiple (LCM) is the smallest number or expression that is a common multiple of two or more numbers or algebraic terms.

We first factorize the given binomials $(x+4{)}^2(x-3{)}^3$ and $(x-1)(x+4)(x-3{)}^2$ as shown below:

$(x+4{)}^2(x-3{)}^3=(x+4)\times (x+4)\times (x-3)\times (x-3)\times (x-3)(x-1)(x+4)(x-3{)}^2=(x-1)\times (x+4)\times (x-3)\times (x-3)$

Now multiply all the factors, using each common factor only once, therefore, the LCM is:

$(x-1)\times (x+4)\times (x+4)\times (x-3)\times (x-3)\times (x-3)=(x-1)(x+4{)}^2(x-3{)}^3$

Hence, the LCM of $(x+4{)}^2(x-3{)}^3$ and $(x-1)(x+4)(x-3{)}^2$ is $(x-1)(x+4{)}^2(x-3{)}^3$.