LCM of 15 and 35
2026-02-28 19:17 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-15-and-35

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Last updated on August 5, 2025

LCM is the smallest common multiple between 2 or more numbers that can divide the numbers evenly. It is a mathematical tool we apply in various fields like making music, planning and scheduling.

What is the LCM of 15 and 35?

LCM of 15 and 35 becomes 105. Let’s find out how to get the LCM. 

How to find the LCM of 15 and 35?

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

LCM of 15 and 35 using the Listing multiples method

 list the multiples of the integers until a common multiple is found. 


 Step 1: List multiples of each number:  


Multiples of 15 = 15,30,45,60,…105,…


Multiples of 35 = 35,70,105,…


 Step 2: Find the smallest multiple from the listed multiples


The least common multiple of the numbers is 105.


LCM(15,35) = 105

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LCM of 15 and 35 using the Prime Factorization

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.


Step 1:  prime factorize the numbers:

15  = 5×3


35= 7×5


Step 2: pick the highest power of each prime factor and multiply the ascertained factors.


— 7,3,5 = LCM, i.e, 105

LCM of 15 and 35 using the Division Method

Step 1: Write the numbers in a row;

Step 2: Divide the row of numbers by a prime number that is evenly divisible into one of the given numbers, and bring down the numbers not divisible by the previous prime number. 

       Step 3: Continue dividing the numbers until the last row of the result is ‘1’. The LCM of the numbers is the product of the prime numbers in the first column, i.e, 


LCM(15,35)=105

Common Mistakes and how to avoid them in LCM of 15 and 35

When we try to find the LCM, kids may commit some mistakes. Look out for these when you are learning the LCM of 15 and 35. 
 

Problem 1

The sprinkler watering system waters every 15 days and the drip watering system waters every 35 days. On which day do they have to be turned on together?

Okay, lets begin

LCM(15,35) = 105
 

Explanation

Both the watering systems have to be turned on together in 105 days. The LCM expresses the smallest common time interval between the digits.

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Problem 2

Verify a=15,b=35 LCM(a,b)×HCF(a,b)=a×b is satisfied.

Okay, lets begin

LCM of 15,35= 105


HCF of 15,35 = 5


LCM(a,b)×HCF(a,b)=a×b 


105×5 = 15×35 


525 = 525
 

Explanation

LHS = RHS, the relationship stands true. 

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Problem 3

The LCM of 5 and x is 10. Find x.

Okay, lets begin

LCM(5,x) = 10


LCM(a,b)=a×b/HCF(a,b)


LCM(5,x)=5×x/1 


5×x = 10 


x = 10/5 = 2 
 

Explanation

The LCM of 5 and 2 is 10. The above is how we find it. x = 2.

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FAQs on the LCM of 15 and 35

1.What is the GCF of 15 and 35 ?

Factors of the numbers; 


15 = 1,3,5,15


35 = 1,5,7,35


GCF(15,35) = 5
 

2.What is the LCM of 15,35 and 45?

15  = 5×3


35= 7×5


45 = 3×3×5 


LCM (15,35,45) = 315 
 

3.What is the LCM of 14 and 35?

14  = 2×7


35= 7×5


LCM(14,35) = 70
 

4.What are the multiples of 35?

The multiples of 35 up to 10–35,70,105,140,175,210,245,280,315 and 350.
 

5.What is the LCM of 35 and 70?

35= 7×5


70= 7×5×2


LCM(35,70) = 70
 

Important glossaries for the LCM of 15 and 35

  • Multiple: product of a number and a natural integer 
  • Prime factor: number one gets after prime factorization any given number 
  • Prime factorization: the process of breaking the number into its prime factors. 

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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.