Question

Find the LCM and HCF of 336 and 54 and verify that LCM $\times$ HCF=product of the two numbers.

Answer 1

336 and 54
$336=2\times 2\times 2\times 2\times 3\times 7=2^4$
$54=2\times 3\times 3\times 3=2\times 3^3$
HCF=Product of the smallest power of each common prime factor in the numbers =$2\times 3=6$
LCM=Product of the greatest power of each prime factor involved in the numbers =$2^4\times 3^3\times 7=3024$
$HCF\times LCM$ = $6\times 3024$ = 18144
Product of two given numbers =$336\times 54$ = 18144
Therefore, it is proved that $LCM\times HCF$ = product of two given numbers.