LCM

# How To Find LCM of 8 and 10? Listing, Division, and Prime Factorization Method

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### How To Find LCM of 8 and 10? Listing, Division, and Prime Factorization Method

LCM of 8 and 10 is 40. LCM of 8 and 10, also known as Least Common Multiple or Lowest Common Multiple of 8 and 10 is the lowest possible common number that is divisible by 8 and 10.

Now, let’s see how to find the LCM of 8 and 10. Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88,… and multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90,… Here, both 40 and 80 are the common numbers in the multiples of 8 and 10, respectively, or completely are divisible by 8 and 10. But, when you have to find the LCM, you must focus on the lowest common number. So, 40 is the lowest common number among all the multiples that is divisible by 8 and 10, and hence the LCM of 8 and 10 is 40.

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## Methods to Find the LCM of 8 and 10

There are three different methods for finding the LCM of 8 and 10. They are:

- Division Method
- Prime Factorization Method
- Listing Method

## LCM of 8 and 10 Using the Division Method

The division method is one of the methods for finding the LCM. To find the LCM of 8 and 10 using the division method, divide 8 and 10 by the smallest prime number which is divisible by any of them. Then the prime factors further obtained will be used to calculate the final LCM of 8 and 10.

Follow the following steps to find the LCM of 8 and 10 using the division method:

**Step 1:**Write the numbers for which you have to find the LCM, that is 8 and 10 in this case, separated by commas.**Step 2**: Now, find the smallest prime number which is divisible by either 8 or 10.**Step 3:**If any of the numbers among 8 and 10 is not divisible by the respective prime number, write that number in the next row just below it and proceed further.**Step 4:**Continue dividing the numbers obtained after each step by the prime numbers, until you get the result as 1 in the entire row.**Step 5:**Now, multiply all the prime numbers and the final result will be the LCM of 8 and 10.

LCM of 8 and 10 can be obtained using the division method:

Prime Factors | First Number | Second Number |

2 | 8 | 10 |

2 | 4 | 5 |

2 | 2 | 5 |

5 | 1 | 5 |

1 | 1 |

So, LCM of 8 and 10 = 2 * 2 * 2 * 5 = 40

## LCM of 8 and 10 Using the Prime Factorization Method

The prime factorization method is one of the methods for finding the LCM. To find the LCM of 8 and 10 using the prime factorization method, follow the following steps:

**Step 1:**Find the prime factors of 8 and 10 using the repeated division method.**Step 2:**Write all the prime factors in their exponent forms. Then multiply the prime factors having the highest power.**Step 3:**The final result after multiplication will be the LCM of 8 and 10.

LCM of 8 and 10 can be obtained using the prime factorization method as:

- Prime factorization of 8 can be expressed as 2 * 2 * 2 = 2
^{1}* 2^{1}* 2^{1}= 2^{3} - Prime factorization of 10 can be expressed as 2 * 5 = 2
^{1}* 5. - So, the LCM of 8 and 10 = 2
^{3 }* 5^{1}= 2 * 2 * 2 * 5 = 40

## LCM of 8 and 10 Using the Listing Method

The listing method is one of the methods for finding the LCM. To find the LCM of 8 and 10 using the listing method, follow the following steps:

**Step 1:**Write down the first few multiples of 8 and 10 separately.**Step 2:**Out of all the multiples of 8 and 10 focus on the multiples that are common to both the numbers, that is, 8 and 10.**Step 3:**Now, out of all the common multiples, take out the smallest common multiple. That will be the LCM of 8 and 10.

LCM of 8 and 10 can be obtained using the listing method:

- Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88,…
- Multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90,…
- Here, it is clear that the least common multiple is 40. So, the LCM of 8 and 10 is 40.

## What Is the Formula for Calculating the LCM of 8 and 10?

LCM of 8 and 10 can be calculated using the formula:

LCM (8, 10) = (8 * 10) / HCF (8, 10),

where HCF is the highest common factor or the greatest common divisor of 8 and 10.

Another formula, using which the LCM of 8 and 10 can be found:

8 * 10 = LCM (8, 10) * HCF (8, 10), that is,

the product of 8 and 10 is equal to the product of its LCM and HCF.

## Problems Based on LCM of 8 and 10

**Question 1: Find the LCM of 8 and 10 using the prime factorization method.****Solution:**

To find the LCM of 8 and 10 using the prime factorization method, first, we will find the prime factors of 8 and 10 using the repeated division method. Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power. The final result after multiplication will be the LCM of 8 and 10.

Prime factorization of 8 can be expressed as 2 * 2 * 2 = 2^{1} * 2^{1} * 2^{1} = 2^{3}

Prime factorization of 10 can be expressed as 2 * 5 = 2^{1} * 5^{1}

So, the LCM of 8 and 10 = 2^{3 }* 5^{1} = 2 * 2 * 2 * 5 = 40

**Question 2: What is the LCM of 8, 10, and 20?****Solution:**

We will find the LCM of 8, 10, and 20 using the division method.

To find the LCM of 8, 10, and 20 using the division method, first, we will find the smallest prime number which is divisible by either 8 or 10 or 20. If any of the numbers among 8, 10, and 20 are not divisible by the respective prime number, we will write that number in the next row just below it and proceed further. We will continue dividing the numbers obtained after each step by the prime numbers until we get the result as 1 in the entire row. We will multiply all the prime numbers and the final result will be the LCM of 8, 10, and 20.

Prime Factors | First Number | Second Number | Third Number |

2 | 8 | 10 | 20 |

2 | 4 | 5 | 10 |

2 | 2 | 5 | 5 |

5 | 1 | 5 | 5 |

1 | 1 | 1 |

So, LCM of 8, 10, and 20 = 2 * 2 * 2 * 5 = 40

**Question 3: If the LCM of two numbers is 40, HCF is 2, and one of the numbers is 10, find the other number.****Solution:**

As we know, the product of two numbers = LCM * HCF

It is given that,

one of the numbers = 10, LCM = 40, and HCF = 2

Let the other number be x.

So, 10 * x = 40 * 2

x = (40 * 2) / 10

x = 80 / 10

x = 8

Hence, the other number is 8.

**Question 4: Find the LCM of 8 and 10 using the listing method.****Solution:**

To find the LCM of 8 and 10 using the listing method, we will first write down the first few multiples of 8 and 10 separately. Out of all the multiples of 8 and 10, we will focus on the multiples which are common to both numbers.

Then, out of all the common multiples, we will take out the smallest common multiple. That will be the LCM of 8 and 10.

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88,…

Multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90,…

Here, the least common multiple is 40.

So, the LCM of 8 and 10 is 40.

**Question 5: What is the least possible number which is divisible by 8 and 10?****Solution:**

There are three methods using which you can find the least possible number which is divisible by 8 and 10.

We will find it using the division method. First, we will find the smallest prime number which is divisible by either 8 or 10. If any of the numbers among 8 and 10 is not divisible by the respective prime number, we will write that number in the next row just below it and proceed further. We will continue dividing the numbers obtained after each step by the prime numbers until we get the result as 1 in the entire row. We will multiply all the prime numbers and the final result will be the LCM of 8 and 10.

Prime Factors | First Number | Second Number |

2 | 8 | 10 |

2 | 4 | 5 |

2 | 2 | 5 |

5 | 1 | 5 |

1 | 1 |

So, LCM of 8 and 10 = 2 * 2 * 2 * 5 = 40

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## Frequently Asked Questions (FAQs)

**Is 80 also considered as the LCM of 8 and 10?**

No, 80 is not considered as the LCM of 8 and 10. 80 is a common multiple of 8 and 10. But, it is not the least common number which is divisible by 8 and 10, and while finding the LCM, you must focus on the lowest common number. So, 40 is the lowest common number divisible by 8 and 10.

**Are LCM and HCF of 8 and 10 the same?**

LCM of 8 and 10 is 40 and HCF of 8 and 10 is 2. So, LCM and HCF of 8 and 10 are not the same.

**What is the LCM of 8 and 10?**

LCM of 8 and 10 is 40.

**Are the LCM of 8 and 10 the same as the LCM of 8, 10, and 20?**

LCM of 8 and 10 are 40 and LCM of 8, 10, and 20 is 40. So, the LCM of 8 and 10 are the same as the LCM of 8, 10, and 20.

**Write the methods to find the LCM of 8 and 10.**

There are 3 major methods for finding the LCM of 8 and 10:

- Division Method
- Prime Factorization Method
- Listing Method

We hope you understand all the basics on how to find the LCM of 8 and 10.

Written by by

Prerit Jain