Question

The LCM of $(x-1)(x-2)and(x-2)(x-7)$ is:

• A. $(x-1)(x-2)$
• B. $(x-1)(x-2)(x-7)$
• C. $(x-2)(x-7)$
• D. $(x-1)(x-7)$

Answer 1

The correct option is B $(x-1)(x-2)(x-7)$

The irreducible factors occuring in $(x-1)(x-2)and(x-2)(x-7)$ are $(x-1),(x-2)and(x-7)$
The greatest exponents of these respectively are 1,1 and 1.
Hence, the LCM = $(x-1{)}^1\times (x-2{)}^1\times (x-7{)}^1=(x-1\left)\right(x-2\left)\right(x-7)$.