Question

Find the LCM and HCF of 336 and 54

• A. LCM = 6
• B. HCF = 3024
• C. LCM = 3024
• D. HCF = 6

Answer 1

Answer: (C), (D)

The correct options are
C LCM = 3024
D HCF = 6

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.