Question

How do you find the LCM of $$7$$ and $$9$$?

Answer 1

Hint: There are various methods for finding the least common multiple of two given numbers. The simplest method to find the least common multiple is by prime factorization method. In the prime factorization method, we first represent the given two numbers as a product of their prime factors and then find the product of all the factors counting the common factors only once.

Complete step by step solution:
To find the least common multiple of $$7$$ and $$9$$, first we find out the prime factors of both the numbers.
We know that $$7$$ is a prime number. So, we get,
Prime factors of $$7$$$=7\times 1$
Prime factors of $$9$$$=3\times 3$
Now, Least common multiple is a product of common factors with highest power and all other non-common factors. We can see that there is no common factor of $$7$$ and $$9$$.
Hence, least common multiple of $$7$$ and $$9$$$=7\times 3\times 3$
$=63$
Hence, the least common multiple of $$7$$ and $$9$$ is $63$.

Note:
Least common multiple (LCM) has wide ranging applications in the real world as well as in mathematical questions. Knowledge of the least common multiple is also used in addition and subtraction of fractions. Highest common factor is the greatest number that divides both the given numbers. Similarly, the highest common factor can also be found by using prime factorization methods as well as using Euclid’s division lemma. Highest common divisor is just a product of common factors with the lowest power. Highest common factor can also be calculated by division method as well as by using Euclid’s division lemma.