Question

If $a=2^3\times 3^2\times 5$ and $b=2^4\times 3\times 7^2$, then which of the following is true?

• A. HCF = $2^3\times 3^2\times 5\times 7$
  LCM = $2^7\times 3^3\times 5\times 7^2$
• B. HCF = $2\times 3\times 5\times 7$
  LCM = $2^2\times 3^2\times 5\times 7^2$
• C. HCF = $2^3\times 3^2$
  LCM = $2^4\times 3^2\times 5\times 7^2$
• D. HCF = $2^3\times 3$
  LCM = $2^4\times 3^2\times 5\times 7^2$

Answer 1

The correct option is D

HCF = $2^3\times 3$
LCM = $2^4\times 3^2\times 5\times 7^2$

HCF is the product of common prime factors with their lowest power.

LCM is the product of prime factors with their highest power.

Given : $a=2^3\times 3^2\times 5$ and $b=2^4\times 3\times 7^2$

$\Rightarrow$ HCF of a and b = $2^3\times 3$ ( Taking the product of lowest powers of common factors)

LCM of a and b = $2^4\times 3^2\times 5\times 7^2$ (Taking the product of prime factors with their highest power)