Question

If two positive integers $a$ and $b$ are written as $a = x^3y^2$ and $b = xy^3$, where $x$ and $y$ are prime numbers, then LCM $(a, b)$ is: (A) $xy$ (B) $xy^2$ (C) $x^3y^3$ (D) $x^2y^2$

Accepted Answer

C. Given two positive integers $a = x^3y^2$ and $b = xy^3$, where $x$ and $y$ are prime numbers. To find the LCM, we take the highest power of each prime factor present in the factorizations of $a$ and $b$. For prime factor $x$, the powers are $x^3$ (from $a$) and $x^1$ (from $b$). The highest power is $x^3$. For prime factor $y$, the powers are $y^2$ (from $a$) and $y^3$ (from $b$). The highest power is $y^3$. Therefore, LCM $(a, b) = x^3y^3$.

LCM of expressions with prime factors

Explanation

Practise this under board exam conditions