Question

How do you use prime factorization to find the LCM of 28 and 42?

Answer 1

Hint: To find the LCM by prime factorization method first we need to write each number as the product of their prime factors. Then we will find the product with the highest power of all prime factors. The obtained product is the LCM of the numbers.

Complete step by step answer:
We have been given two numbers 28 and 42.
We have to find the LCM of given numbers by using the prime factorization method.
We know that LCM means least common multiple. LCM is defined as the smallest integer which is a multiple of two or more numbers.
First we will write each number as a product of all prime factors. Then we will get
Prime factors of $28=2\times 2\times 7$
Prime factors of $42=2\times 3\times 7$
Now, we will find the product of the highest powers of all prime factors. Then we will get
LCM of 28 and 42 $=2\times 2\times 3\times 7=84$

Hence we get the LCM of 28 and 42 as 84.

Note: Students may calculate the LCM as $2\times 3\times 7=42$ which is incorrect because 2 appears two times and we need to multiply the highest power. Alternative methods to find the LCM are listing the multiples, division method, and least common multiple formula. If we know the GCD of two numbers then we will use the LCM formula to find the LCM of the given numbers.