Question

If $a=2^3\times 3^4\times 7^2$and $b=2^3\times 3^2\times 5^3,$ then which of the following is true?

• A. $HCF=2^3\times 3^2;LCM=2^3\times 3^4\times 5^3\times 7^2$
• 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. $LCM=2^2\times 3^2;HCF=2^3\times 3^3\times 5^3\times 7^2$

Answer 1

The correct option is A $HCF=2^3\times 3^2;LCM=2^3\times 3^4\times 5^3\times 7^2$

HCF = Product of the smallest powers of each common prime factor in the numbers.
LCM = Product of the largest powers of each common prime factor in the numbers.
The common prime factors of $a$ and $b$ are 2 and 3.
$\text{Thus,}HCF=2^3\times 3^2.$
All the prime factors of $a$ and $b$ are 2,3,5 and 7.
$\text{Thus,}LCM=2^3\times 3^4\times 5^3\times 7^2$