Question

Find the HCF and LCM of the $60$ and $72$ by the fundamental theorem of arithmetic.

• A. HCM = $12$, LCM = $360$
• B. HCM = $12$, LCM = $340$
• C. HCM = $22$, LCM = $360$
• D. HCM = $12$, LCM = $260$

Answer 1

The correct option is A HCM = $12$, LCM = $360$

Theorem (Fundamental Arithmetic Theorem) : Every composite number can be expressed ( factorized) as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur.

So, let's factorize

$60=3\times 2^2\times 5$
$72=2^3\times 3^2$

$HCF=2^2\times 3=12$
$LCM=3^2\times 2^3\times 5=360$