Question

Which of the following correctly represents the HCF and LCM of 4500 and 10584?

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

Answer 1

The correct option is D

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

Prime Factorisation of the numbers 4500 and 10584 is given by
$4500=2^2\times 3^2\times 5^3$
$10584=2^3\times 3^3\times 7^2$
The common prime factors of 4500 and 10584 are 2 and 3. The lowest power of 2 is 2 and of 3 is also 2. Thus, the HCF = $2^2\times 3^2$
The prime factors of 4500 and 10584 are 2,3,5 and 7. The highest power of 2 is 3, of 3 is 3, of 5 is 3 and of 7 is 2. Thus, the LCM = $2^3\times 3^3\times 5^3\times 7^2$