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146 LearnersLast updated on November 30th, 2024
LCM of 11 and 13
The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 11 and 13. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music. In this article, let’s now learn to find LCMs of 11 and 13.
What is LCM of 11 and 13
We can find the LCM using listing multiples method, prime factorization method and the long division method. These methods are explained here, apply a method that fits your understanding well.
LCM of 11 and 13 using listing multiples method
Step 1: List the multiples of each of the numbers;
11 = 11,22,33,…143
13 = 13,26,39,…143
Step 2: Find the smallest number in both the lists
LCM (11,13)=143
LCM of 11 and 13 using prime factorization method
Step 1:Prime factorize the numbers
11 = 11×1
13 = 13×1
Step 2:find highest powers
Step 3:Multiply the highest powers of the numbers
LCM(11,13) = 143
LCM of 11 and 13 using division method
- Write the numbers in a row
- Divide them with a common prime factor
- Carry forward numbers that are left undivided
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM (11,13) = 143
Common mistakes and how to avoid them in LCM of 11 and 13
LCM of 11 and 13 Examples
Problem 1
For any two integers a and b, the LCM is related to their product by the equation: LCM(a, b)×GCF(a, b)=a×b Use this formula to verify if the LCM of 11 and 13, when divided by 11, is equal to the product of 13 and the GCF of 11 and 13.
Explanation
Problem 2
If N is the least number divisible by both 11 and 13, and the sum of the digits of N equals 8, what is N?
Explanation
Problem 3
A light flashes every 11 seconds and another light flashes every 13 seconds. Both lights flash at the same time. After how many seconds will they flash together again?
Explanation
Problem 4
A number X is divisible by both 11 and 13. The number is less than 500. What is the largest possible value of X?
Explanation
FAQs on LCM of 11 and 13
1.What is the GCF of 11 and 13 ?
2.What is the LCM of 3 and 11?
3.What is the LCM of 11 and 15?
4.What is the LCM of 9 and 15?
5.What is the LCM of 8 and 12?
Important glossaries for LCM of 11 and 13
- Multiple: the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75.
- Prime Factor: A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind.
- Prime Factorization: breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5.
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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.
