Question

The HCF of 3240, 3600 and a third number is 36, and their LCM is $2^4\times 3^5\times 5^2\times 7^2$. The third number is

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

Answer 1

The correct option is B $2^2\times 3^5\times 7^2$

$3240=2^3\times 3^4\times 5;3600=2^4\times 3^2\times 5^2$

HCF = $2^3\times 3^2$

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

Since HCF is the product of lowest powers of
common factors third number should have
$2^3\times 3^2$ as factor
LCM is the product of the highest powers of all
factors therefore third number should
have $3^5\times 5^7$ as its factors
$\therefore$ Third number = $2^2\times 3^5\times 7^2$