# Given that HCF (306, 657) = 9, find LCM (306, 657)

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Given, HCF (306, 657) = 9

To find, LCM of 306 and 657

We know that, LCM×HCF = Product of the two numbers.

Now we will put the given values in the above mentioned formula:

LCM × 9 = 306 × 657

LCM × 9 = 201042

LCM = 201042 ÷ 9

LCM = 22338

Therefore, the LCM of 306 and 657 is 22338.

## LCM of 306 and 657 by Prime Factorization

We can also find the LCM of 306 and 657, by doing prime factorization of 306 and 657.

So, the Prime Factorization of 306 is 2 × 3 × 3 × 17

And the Prime Factorization of 657 is 3 × 3 × 73

As we can see, 3 is common in the prime factorization of 306 and 657. So we will take their product i.e. 3 × 3 = 9.

The remaining numbers of the prime factorization of 306 and 657 are 2, 17, and 73. Now, we will multiply these numbers to get the LCM of 306 and 657.

So, the LCM of 306 and 657 = 2 × 17 × 73 × 9 = 22338.

## What are LCM, HCF, and Prime Factorization?

LCM: It stands for Least Common Multiple. It is the least common factor of two integers a and b is the smallest positive integer that is divisible by both a and b.

Example – LCM of 2 and 5

• Take multiples of 2 – 2,4,6,8,10,12,14
• Now, take multiples of 5 – 5,10,15,20,25
• We can see that 10 is the lowest common factor of 2 and 5. Hence, 10 is the LCM of 2 and 5.

HCF: Highest Common Factor is called HCF. It is the greatest number among all the common factors of the given numbers OR it is the greatest common factor that can completely divide the given numbers.

Example – HCF of 20 and 25

When we find the highest common factor of 20 and 25, it is 5 because 5 is the only largest number that can divide both 20 and 25 completely.

Prime Factorization: It is defined as a method of finding the prime factors of a number such that the prime numbers divide that number completely.

Example – Prime factorization of 18 is 2 × 3 × 3.

Summary:

## Given that HCF (306, 657) = 9, find LCM (306, 657)

The LCM of 306 and 657 for given HCF (306, 657) is 22338. We can determine the LCM of 306 and 657 by using the formula (LCM×HCF = Product of the two numbers). In the formula, put 9 in place of ‘HCF’ and the product of 306 and 657 in place of ‘Product of the two numbers’. Then divide the product of 306 and 657 by 9 to get the LCM of 306 and 657.

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