Question

Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of $816$ and $170$.

• A. L.C.M. $=4080$ and H.C.F $=34$
• B. L.C.M. $=8160$ and H.C.F $=68$
• C. L.C.M. $=2048$ and H.C.F $=62$
• D. L.C.M. $=2040$ and H.C.F $=72$

Answer 1

The correct option is A L.C.M. $=4080$ and H.C.F $=34$

According to the fundamental theorem of arithmetic every composite number can be factorised as a product of primes and this factorization is unique apart from the order in which the prime factor occurs.

• Fundamental theorem of arithmetic is also called unique factorization theorem.
  
• Composite number = product of prime numbers.
  
• Any Integer greater than 1, either be a prime number or can be written as a product of prime factors.
  

The prime factors of $816=2\times 2\times 2\times 2\times 3\times 17=2^4\times 3\times 17$

The prime factors of $170=2\times 5\times 17$

LCM of $816$ and $170=2^4\times 3\times 5\times 17=4080$

HCF of $816$ and $170=2\times 17=34$

Option A.