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134 LearnersLast updated on November 29th, 2024
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
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?
Explanation
Problem 2
Elaborate on the relationship between HCF and LCM of 26 and 39.
Explanation
Problem 3
If the HCF of 6 and 18 is 6, using the relationship between 6 and 18, find the LCM.
Explanation
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 ?
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
: She loves to read number jokes and games.
