LCM of 10 and 16
2026-02-28 09:00 Diff
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Last updated on August 5, 2025

Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 10 and 16. By learning the following tricks, you can learn the LCM of 10 and 16 easily.

What Is the LCM of 10 and 16?

The LCM of 10 and 16 is 80. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.
 

How to find the LCM of 10 and 16?

We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:


Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method


Now let us delve further into these three methods and how it benefits us.
 

LCM of 10 and 16 Using Listing of Multiples Method

In this method, we will list all the multiples of 10 and 16. Then we will try to find a multiple that is present in both numbers.


For example, 


Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100,…


Multiples of 16:
16,32,48,64,80,96,112,128,144,160,…

The LCM of 10 and 16 is 80. 80 is the smallest number which can be divisible by both 10 and 16.
 

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LCM of 10 and 16 Using Prime Factorization

To find the LCM of 10 and 16 using the prime factorization method, we need to find out the prime factors of both the numbers. Then multiply the highest powers of the factors to get the LCM. 


Prime Factors of 10 are: 21 × 51.


Prime Factors of 16 are: 24.


Multiply the highest power of both the factors: 24 × 51  = 2 × 2 × 2 × 2 × 5 = 80


Therefore, the LCM of 10 and 16 is 80.
 

LCM of 10 and 16 Using Division Method

To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.


For finding the LCM of 10 and 16 we will use the following method.

By multiplying the prime divisors from the table, we will get the LCM of 10 and 16.


2 × 2 × 2 × 2 × 5 = 80. The LCM of 10 and 16 is 80

Common Mistakes and How to Avoid Them in LCM of 10 and 16.

Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
 

Problem 1

Two pipes fill a tank. Pipe A fills it in 10 minutes, and Pipe B in 16 minutes.If both pipes are opened at the same time, how long will it take for them to fill the tank together?

Okay, lets begin

LCM of 10 and 16 is 80. 


Calculate the rate at which each tank is filled by the pipes 


Pipe A's rate: 1/10 per minute.
Pipe B's rate: 1/16 per minute.


Combined rate: 1/10 + 1/16 = (8+5) / 80 = 13/80


Time to fill the tank: 80/13 ≈ 6.15 minutes.
 

Explanation

The LCM helps determine a common time interval. By using rates and combining them, we get the total time to complete the task.
 

Well explained 👍

Problem 2

Calculate the number of cycles when two rotating gears A and B, with rotations every 10 and 16 seconds respectively, will align. Use the formula Number of cycles=LCM/Rotation Time.

Okay, lets begin

LCM (10,16) = 80


Cycles for Gear A to complete alignment: 80 / 10 = 8


Cycles for Gear B to complete alignment: 80 / 16 = 5
 

Explanation

 This uses the formula by applying the LCM as the period of alignment. The division yields each gear's cycles until alignment.
 

Well explained 👍

Problem 3

A marathon track has two checkpoints, C and D. Runners cross checkpoint C every 10 minutes and checkpoint D every 16 minutes. If a runner crosses both checkpoints together every ___ minutes, find the missing time.

Okay, lets begin

LCM (10,16) = 80
Thus, the missing time is 80 minutes.
 

Explanation

The problem involves determining a common interval for crossing both checkpoints. By calculating the LCM, we find that both checkpoints align every 80 minutes.
 

Well explained 👍

FAQs on the LCM of 10 and 16

1. Is 10 a prime number?

No, 10 is not a prime number. Because it has more than two factors.
 

2. What is the GCF of 10 and 16?

Factors of 10 = 1,2,5,10 
Factors of 16 = 1,2,4,8,16 
GCF (10,16) = 2
 

3. What is the LCM of 10 and 15?

 LCM is the smallest number divisible by 10 and 15. LCM (10,15) = 30.

4.What are the first five common multiples of 10 and 16?

The common multiples in their order of appearance up to the count of five are → 80,160,240,320, and 400. LCM (10,16) = 80
 

5.What is the LCM of 6 and 10?

(10,6) = 60. 60 is the smallest number that appears commonly on the lists of the numbers 6 and 10. 
 

Important Glossaries for the LCM of 10 and 16

  • Prime Number: Any number that has only 2 factors is called a prime number.For 5 and 7, only common factors are 1 and the number itself.
  • Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4,8 and 10. 
  • Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
     

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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.