151 LearnersLast updated on May 26th, 2025
LCM of 26 and 39
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 26 and 39. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
How to find the LCM of 26 and 39?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 26 and 39 using the Listing multiples method
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Step 1:Write down the multiples of each number:
Multiples of 26 = 26,52,78,…
Multiples of 39 = 39,78,…
Step 2: Ascertain the smallest multiple from the listed multiples
The least common multiple of the numbers is 78.
LCM (26,39) =78
LCM of 26 and 39 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: Find the prime factors of the numbers:
Prime factorization of 26 = 13×2
Prime factorization of 39= 13×3
Step 2: Take the highest power of each prime factor and multiply the ascertained factors.
LCM(26,39) = 78
LCM of 26 and 39 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step1: Write down the numbers in a row;
Step2: 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.
Step3: The LCM of the numbers is the product of the prime numbers in the first column, i.e,
LCM(26,39) = 78
Common Mistakes and how to avoid them while finding the LCM of 26 and 39
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 26 and 39, make a note while practicing.
Mistake 1
Confusing between LCM and HCF of the numbers 26 and 39
It is common for one to be confused between the HCF (Highest common factor) and LCM (least common multiple). LCM is the smallest number divisible by 26 and 39 while, the largest number that divides them both is the HCF.
A simple trick to remember is that the HCF is going to be a relatively smaller number, it deals with divisors.
LCM of 26 and 39, examples
Problem 1
S goes to the office canteen every 26 days, and A goes every 39 days. After how many days will they meet on the same day again?
The LCM of 26 and 39 is 78.
Explanation
They will meet again on the same day in 72 days. The LCM of 26 and 39 is 42, which expresses the smallest common time interval between the digits.
Problem 2
Elaborate on the relationship between HCF and LCM of 26 and 39.
The relationship between HCF and LCM can be verified using this formula; HCF(a,b)×LCM(a,b) = a×b
HCF of 26,39 = 13
LCM of 26,39 = 78
Now apply the formula,
HCF(a,b)×LCM(a,b) = a×b
HCF(26,39)×LCM(26,39) = 26×39
13×78 = 26×39
1014 = 1014
Explanation
The above explains the relationship between the HCF and the LCM of 26 and 39. The given formula works to verify the relationship between the HCF and LCM for any given pair of numbers.
Problem 3
If the HCF of 6 and 18 is 6, using the relationship between 6 and 18, find the LCM.
Given values;
HCF = 6
a = 6
b = 18
Using the formula;
LCM (a,b)=a×b/HCF(a, b)
LCM (6,18)= 6×18/6 =18
Explanation
The relationship between HCF and LCM, as explained above allows us to find the LCM without direct calculation.
FAQ’s on LCM of 26 and 39
1.What is the LCM of 24 and 32?
2.What is the LCM of 26,30 and 36?
3.What is the LCM of 36,48,72?
4.What is the HCF of 26 and 39?
5.What is the LCM of 26,39 and 60 ?
6.How can children in United States use numbers in everyday life to understand LCM of 26 and 39?
7.What are some fun ways kids in United States can practice LCM of 26 and 39 with numbers?
8.What role do numbers and LCM of 26 and 39 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 26 and 39 skills?
Important glossaries on the LCM of 26 and 39
- Multiple: A product of a number and any integer.
- Prime Factor: A prime factor is a natural number, other than 1, whose only factors are 1 and itself.
- Prime Factorization: The process of breaking down a number into its prime factors.
- Co-prime numbers: A number is co-prime when the only positive integer that is a divisor of them both is 1.
- Greatest Common Divisor (GCD): The largest positive integer that divides each of two or more integers without leaving a remainder.
- Relatively Prime Numbers: Two numbers that have no common factors other than 1.
- Fraction: A number representing 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
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