LCM

# How To Find LCM of 15 and 20?Listing, Division, and Prime Factorization Method

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### How To Find LCM of 15 and 20?Listing, Division, and Prime Factorization Method

LCM of 15 and 20 is 60. LCM of 15 and 20, also known as Least Common Multiple or Lowest Common Multiple of 15 and 20 is the lowest possible common number that is divisible by 15 and 20.

Now, let’s see how to find the LCM of 15 and 20. Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135,… and multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, 180,… Here, both 60 and 120 are the common numbers in the multiples of 15 and 20, respectively, or that are divisible by 15 and 20. But, when you have to find the LCM, you must focus on the lowest common number. So, 60 is the lowest common number among all the multiples that is divisible by 15 and 20, and hence the LCM of 15 and 20 is 60.

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## Methods to Find the LCM of 15 and 20

There are three different methods for finding the LCM of 15 and 20. They are:

- Listing Method
- Prime Factorization Method
- Division Method

## LCM of 15 and 20 Using the Listing Method

The listing method is one of the methods for finding the LCM. To find the LCM of 15 and 20 using the listing method, follow the following steps:

**Step 1:**Write down the first few multiples of 15 and 20 separately.**Step 2:**Out of all the multiples of 15 and 20 focus on the multiples that are common to both the numbers, that is, 15 and 20.**Step 3:**Now, out of all the common multiples, take out the smallest common multiple. That will be the LCM of 15 and 20.

LCM of 15 and 20 can be obtained using the listing method:

- Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135,…
- Multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, 180,…

Here, it is clear that the least common multiple is 60. So, the LCM of 15 and 20 is 60.

## LCM of 15 and 20 Using the Prime Factorization Method

The prime factorization method is one of the methods for finding the LCM. To find the LCM of 15 and 20 using the prime factorization method, follow the following steps:

**Step 1:**Find the prime factors of 15 and 20 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 15 and 20.

LCM of 15 and 20 can be obtained using the prime factorization method as:

- Prime factorization of 15 can be expressed as 3 * 5 = 3
^{1}* 5^{1} - Prime factorization of 20 can be expressed as 2 * 2 * 5 = 2
^{2}* 5^{1}

So, the LCM of 15 and 20 = 3^{1} * 2^{2 }* 5^{1} = 3 * 2 * 2 * 5 = 60

## LCM of 15 and 20 Using the Division Method

The division method is one of the methods for finding the LCM. To find the LCM of 15 and 20 using the division method, divide 15 and 20 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 15 and 20.

Follow the following steps to find the LCM of 15 and 20 using the division method:

**Step 1:**Write the numbers for which you have to find the LCM, that is 15 and 20 in this case, separated by commas.**Step 2:**Now, find the smallest prime number which is divisible by either 15 or 20.**Step 3:**If any of the numbers among 15 and 20 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 15 and 20.

LCM of 15 and 20 can be obtained using the division method:

Prime Factors | First Number | Second Number |

2 | 15 | 20 |

2 | 15 | 10 |

3 | 15 | 5 |

5 | 5 | 5 |

1 | 1 |

So, LCM of 15 and 20 = 2 * 2 * 3 * 5 = 60

## What Is the Formula for Finding the LCM of 15 and 20?

LCM of 15 and 20 can be calculated using the formula:

LCM (15, 20) = (15 * 20) / HCF (15, 20),

where HCF is the highest common factor or the greatest common divisor of 15 and 20.

Another formula, using which the LCM of 15 and 20 can be found:

15 * 20 = LCM (15, 20) * HCF (15, 20), that is,

the product of 15 and 20 is equal to the product of its LCM and HCF.

## Problems Based on LCM of 15 and 20

**Question 1: If the LCM of two numbers is 60, HCF is 5, and one of the numbers is 15, find the other number.****Solution:**

As we know,

Product of two numbers = LCM * HCF

It is given that,

One of the numbers = 15, LCM = 60, and HCF = 5

Let the other number be x.

So, 15 * x = 60 * 5

x = (60 * 5) / 15

x = 300 / 15

x = 20

Hence, the other number is 20.

**Question 2: Find the LCM of 15 and 20 using the listing method.****Solution:**

To find the LCM of 15 and 20 using the listing method, first, we will write down the first few multiples of 15 and 20 separately. Out of all the multiples of 15 and 20, 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 15 and 20.

**Step 1:**Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135,…**Step 2:**Multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, 180,…**Step 3:**Here, the least common multiple is 60. So, the LCM of 15 and 20 is 60.

**Question 3: What is the LCM of 15, 20, and 30?****Solution:**

We will find the LCM of 15, 20, and 30 using the prime factorization method:

To find the LCM of 15, 20, and 30 using the prime factorization method, first, we will find the prime factors of 15, 20, and 30 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 15, 20, and 30.

**Step 1:**Prime factorization of 15 can be expressed as 3 * 5 = 3^{1}* 5^{1}**Step 2:**Prime factorization of 20 can be expressed as 2 * 2 * 5 = 2^{2}* 5^{1}**Step 3:**Prime factorization of 30 can be expressed as 2 * 3 * 5 = 2^{1}* 3^{1}* 5^{1}**Step 4:**So, the LCM of 15, 20, and 30 = 2^{2 }* 3^{1}* 5^{1}= 2 * 2 * 3 * 5 = 60

**Question 4: What is the least possible number which is divisible by 15 and 20?****Solution:**

There are three methods using which you can find the least possible number which is divisible by 15 and 20.

We will find it using the division method. First, we will find the smallest prime number which is divisible by either 15 or 20. If any of the numbers among 15 and 20 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 15 and 20.

Prime Factors | First Number | Second Number |

2 | 15 | 20 |

2 | 15 | 10 |

3 | 15 | 5 |

5 | 5 | 5 |

1 | 1 |

So, LCM of 15 and 20 = 2 * 2 * 3 * 5 = 60

**Question 5: Find the LCM of 15 and 20 using the prime factorization method.****Solution:**

To find the LCM of 15 and 20 using the prime factorization method, first, we will find the prime factors of 15 and 20 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 15 and 20.

**Step 1:**Prime factorization of 15 can be expressed as 3 * 5 = 3^{1}* 5^{1}**Step 2:**Prime factorization of 20 can be expressed as 2 * 2 * 5 = 2^{2}* 5^{1}**Step 3:**So, the LCM of 15 and 20 = 3^{1}* 2^{2 }* 5^{1}= 3 * 2 * 2 * 5 = 60

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## Frequently Asked Questions (FAQs)

**Are LCM and HCF of 15 and 20 the same?**

LCM of 15 and 20 is 60 and HCF of 15 and 20 is 5. So, LCM and HCF of 15 and 20 are not the same.

**What is the LCM of 15 and 20?**

LCM of 15 and 20 is 60.

**Write the methods to find the LCM of 15 and 20.**

There are 3 major methods for finding the LCM of 15 and 20:

- Listing Method
- Prime Factorization Method
- Division Method

**Is 120 also considered as the LCM of 15 and 20?**

No, 120 is not considered as the LCM of 15 and 20. 150 is a common multiple of 15 and 20. But, it is not the least common number which is divisible by 15 and 20, and while finding the LCM, you must focus on the lowest common number. So, 60 is the lowest common number divisible by 15 and 20.

**Are the LCM of 15 and 20 the same as the LCM of 15, 20, and 30?**

LCM of 15 and 20 is 60 and LCM of 15, 20, and 30 is 60. So, the LCM of 15 and 20 are the same as the LCM of 15, 20, and 30.

We hope you understand all the basics on how to find the LCM of 15 and 20.

Written by by

Prerit Jain