Question

The LCM of $(x-3)(x-5)and(x-5)(x-7)$ is:

• A. $(x-3)(x-5)(x-7)$
• B. $(x-3)(x-5)$
• C. $(x-3)(x-7)$
• D. $(x-5)(x-7)$

Answer 1

The correct option is A $(x-3)(x-5)(x-7)$

The irreducible factors occuring in $(x-3)(x-5)and(x-5)(x-7)$ are $(x-3),(x-5)and(x-7)$
The greatest exponents of these respectively are 1,1 and 1.
Hence, the LCM = $(x-3{)}^1\times (x-5{)}^1\times (x-7{)}^1=(x-3\left)\right(x-5\left)\right(x-7)$.