Question

Find the LCM and HCF of $77,99$.

Answer 1

Hint: In this question we have been given two numbers for which we have to find the lowest common multiple and the highest common factor. The LCM is the lowest number which is divisible by two or more numbers and the HCF is the highest number which divides two or more numbers completely without any remainder.

Complete step-by-step solution:
We have to find the LCM and HCF of $77,99$.
We will solve this question by using the prime factorization method. In this method we will write both the numbers as a product of prime numbers. We will then write the common factors and the remaining factors as a product to get the highest common factor and the product of the common factors will give us the lowest common multiple.
We can write the number $77$ as:
$\Rightarrow 77=7\times 11$
We can write the number $99$ as:
$\Rightarrow 99=3\times 3\times 11$
Now we can see from the above factors that both the numbers have the same factor which is $11$ and no other therefore, we can conclude that the highest common factor of both the numbers is $11$.
In the general notation it can be written as:
$\Rightarrow HCF\left( 77,99 \right)=11$
Now for the highest common factor, we have the same factor $11$ and we are left with $3$ which occurs two times and $7$ which occurs one time.
On multiplying them, we get:
$\Rightarrow 3\times 3\times 7\times 11$
On multiplying, we get:
$\Rightarrow 693$, which is the required highest common factor.
In the general notation it can be written as:
$\Rightarrow LCM\left( 77,99 \right)=693$
Therefore, we have $HCF\left( 77,99 \right)=11$ and $LCM\left( 77,99 \right)=693$, which is the required solution.

Note:It is to be remembered that the basic definition of lowest common multiple and highest common factor should be remembered. The highest common factor of numbers is used for simplification purposes in an equation and the lowest common multiple is used to simplify fractions during their operation.