LCM of 15 and 20
2026-02-28 10:33 Diff
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Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 15 and 20. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 15 and 20?

How to find the LCM of 15 and 20

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

LCM of 15 and 20 using the Listing multiples method

To ascertain the LCM, list the multiples of the integers until a common multiple is found. 

Steps:

1. Writedown the multiples of each number: 

Multiples of 15 = 15,30,45,60,…

Multiples of 20 = 20,40,60,80…

2. Ascertain the smallest multiple from the listed multiples of 15 and 20.

The LCM (The Least common multiple) of 15 and 20 is 60. i.e., 60 is divisible by 15 and 20 with no reminder.

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LCM of 15 and 20 using the Prime Factorization

This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.

Steps: 

1. Find the prime factors of the numbers:

  • Prime factorization of 15 = 3×5
  • Prime factorization of 20 = 2×2×5  

2. Take the highest power of each prime factor:

— 2,3,2,5

3. Multiply the ascertained factors to get the LCM: 

LCM (8,12) = 2×2×3×5 = 60

LCM of 15 and 20 using the Division Method

The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 

Steps:

1. Write down the numbers in a row;

2. Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

3. The LCM of the numbers is the product of the prime numbers in the first column, i.e., 

3×2×2×5= 60

LCM (15,20) = 60

Common Mistakes and how to avoid them while finding the LCM of 15 and 20

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 15 and 20 make a note while practicing.

Problem 1

1. Motorboat A and motorboat B take trips every 8 minutes and 20 minutes at the lake at the same time. In how long will they arrive together again?

Okay, lets begin

The LCM of 15 and 20 = 60

Explanation

The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the motorboats at the same time, which is in 60 minutes.

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Problem 2

The Newsmail and The City Chronicles publish their newsletters every 8 days and 20 days, respectively. They publish today, on September 1, how many days will it be before they publish together again?

Okay, lets begin

Find the LCM of 15 and 20: LCM (15,20) = 60

Explanation

They will publish together again in 60 days. The LCM of 15 and 20 is 60, which expresses the smallest common time interval between the digits.

Well explained 👍

Problem 3

A bakery sells apple juice and orange juice in bottles. The apple juice bottles are delivered in packs of 15, and the orange juice bottles in packs of 20. What is the least number of bottles of each type of juice that needs to be bought that they have an equal number of apple and orange juice?

Okay, lets begin

We derive the number by finding the LCM of 15 and 20: LCM (15,20) = 60

Explanation

The smallest number of bottles of each type to be brought is 40, so they have an equal number of both. The LCM of 15 and 20 is 60, which expresses the smallest common number between the digits.

Well explained 👍

Problem 4

Mr. S has two kinds of plants that need watering. The lemon plant needs to be watered every 15 days, and the orange plant needs to be watered every 20 days. If both the plants are watered today, in how many days will Mr. S water them together again?

Okay, lets begin

The LCM(15,20) = 60.

Explanation

Mr. S needs to water the plants on the 60th day. The LCM of 15 and 20 is 60, which expresses the smallest common time interval between the digits.

Well explained 👍

FAQ’s on 15 and 20

1.Is multiplying 15 and 20 the correct way to find the LCM?

No, multiplying gives you the product of the numbers, in this case,300. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.

2.Why is the LCM of 15 and 20, not 20?

20 is not a multiple of 15, so it can’t be the LCM. LCM has to be the smallest number that both 15 and 20 can divide without any reminders, which is 60.

3.What is the LCM formula using the HCF?

  • The method below elaborates on how to derive the LCM using HCF (Highest common factor). An example is also attached to check the validity.  

LCM (a, b)= a×b/HCF(a, b)

For the given numbers 15 and 20, HCF(15,20)=5

So, LCM(15,20)=15×20/5= 60

By following the above, we can state that the LCM of numbers 15 and 20 can be found using their HCF, which is 5.

4.Is the LCM of 15 and 20 always a multiple of their HCF?

The LCM is always a multiple of HCF. For the numbers 15 and 20, the HCF is 5, and 60 (the LCM) is a multiple of 5.

5.What do the numbers 15 and 20 have in common?

15 and 20 share common factors, i.e., multiples of the numbers. 

Common factors;

  • 15 = 1,3,5 and 15 
  • 20 =1,2,4,5,10 and 20. 
  • Common factors —> 1 and 5 (Also their common prime factors)

Important glossaries for the LCM of 15 and 20

  • Multiple: A number and any integer multiplied. 
  • Prime Factor: A natural number (other than 1) that has factors that are one and itself.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 
  • Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 
  • Relatively Prime Numbers: Numbers that have no common factors other than 1.
  • Fraction: A representation of a part of a whole.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.