Question

Find the LCM and HCF of the following pair of integers and verify that LCM*HCF = Product of the two numbers: $ 777 $ and $ 1147. $

Answer 1

Hint: To find LCM, find all prime factors of the given number, list them as many as they occur by the given number. Multiply the list of prime factors to find the LCM.
To find HCF, multiply all the common factors from both the lists of the given numbers we will get HCF.

Complete step-by-step answer:
Given numbers in the question are $ 777 $ and $ 1147. $
The prime factorization of $ 777 $ and $ 1147. $ gives:
 $ \Rightarrow 777 = 3 \times 7 \times 37 $
 $ \Rightarrow 1147 = 31 \times 37 $
So, the HCF of the given two numbers is $ 37 $ .
Now ,
The LCM of given numbers, $ $
 $
   \Rightarrow 3 \times 7 \times 31 \times 37 \\
   \Rightarrow 24087 \;
  $
Now, we have to verify,
LCM of $ \left[ {a,b} \right] $ $ \times $ HCF of $ \left[ {a,b} \right] $ = Product of the two numbers $ \left[ {a \times b} \right] $
LHS=
LCM $ \times $ HCF
 $ \Rightarrow $ $ 24087 \times 37 $
 $ \Rightarrow 891219 $
RHS=
Product of two numbers
 $
   \Rightarrow 777 \times 1147 \\
   \Rightarrow 891219. \;
  $
Therefore, LHS=RHS.
So, the product of two numbers is equal to the product of LCM and HCF.

Note: $ \Rightarrow $ The HCF defines the greatest factor present in between given two or more numbers, whereas LCM defines the least number which is exactly divisible by two or more numbers.
 $ \Rightarrow $ HCF is also called the greatest common factor (GCF) and LCM is also called the Least Common Divisor.