Question

Find the least common multiple of 63, 70 and 77?

Answer 1

Hint: Least common multiple of two numbers means the smallest number that is multiple of both the numbers. So, to find the L.C.M of 63, 70 and 77 we will be using the prime factorization method. Prime factorization method is expressing a number as a product of only prime numbers used for making that number.

Complete step-by-step answer:
In this question, we are given 3 numbers 63, 70 and 77 and we have to find their least common multiple.
First of all, what is the least common multiple?
Least common multiple of two numbers also known as L.C.M is the smallest number that is a multiple of both the given numbers. For example: 2 and 3. Now, the multiples of 2 are 2, 4, 6… and multiples of 3 are 3, 6, 9… Here, the smallest common multiple between these two numbers is 6. Hence, the L.CM of 2 and 3 is 6.
Here, we have to find the smallest number that is a multiple of 63, 70 and 77.
Finding L.C.M using Prime Factorization:
First, write the prime factors of 63.
$ \Rightarrow $Prime Factors of 63: $3 \times 3 \times 7$
$ \Rightarrow $Prime factors of 70: $2 \times 5 \times 7$
$ \Rightarrow $Prime factors of 77: $7 \times 11$
Here, the LCM will be the product of all these factors but we have to take 7 only once as it is common in all 3 numbers.
Therefore, the L.C.M of 63, 70 and 77 is $3 \times 3 \times 7 \times 2 \times 5 \times 11 = 6930$.

Note: We can also find the L.C.M using the methods of multiples. In this, we have to write the multiples of the given numbers and find out the first common number between them. But when we are given bigger numbers, using prime factorization is more easy to use as compared to the method of multiples.