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149 LearnersLast updated on November 30th, 2024
LCM of 11 and 12
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 11 and 12. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. In our daily life, we use application of LCM for setting alarms in our clock or synchronization of traffic lights.
What is the LCM of 11 and 12?
The LCM of 11 and 12 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
How to Find the LCM of 11 and 12?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 11 and 12 using the Listing Multiples Method
The LCM of 11 and 12 can be calculated using the following steps:
Step 1: Write down the multiples of each number
Multiples of 11 = 11,22,33,44,55,66,77,88,99,110,121,132,…
Multiples of 12 = 12,24,36,48,60,72,84,96,108,120,132,…
Step 1: Ascertain the smallest multiple from the listed multiples
The smallest common multiple is 132
Thus, LCM(11, 12) = 132
LCM of 11 and 12 using the Prime Factorization Method
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:List the prime factors of each of the given numbers;
Prime factorization of 11 = 11 (since 11 is prime)
Prime factorization of 12 = 2 × 2 × 3
Take the highest powers of each prime factor and multiply the highest powers to get the LCM:
— LCM(11, 12) = 2² × 3 × 11 = 132
LCM of 11 and 12 using the Division Method
This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.
Step 1: Write the numbers. Divide by common prime factors and multiply the divisors.
Step 2: continue till we get 1 as remainder.
2 × 2 × 3 × 11 = 132
Thus, LCM(11, 12) = 132
Common Mistakes and how to avoid them in LCM of 11 and 12
LCM of 11 and 12, examples
Problem 1
A movie theater alternates between a crime film and a children’s film. The crime film is shown every 11 days and the children’s film is shown every 12 days. In how many days will they both be screened together?
Explanation
Problem 2
The LCM of a and b is 132. a = 12, b = ?
Explanation
Problem 3
What is the smallest number that is divisible by both 11 and 12?
Explanation
FAQs on LCM of 11 and 12
1.What are the multiples of 11 and 12?
2.What is the LCM of 11 and 11?
3.What is the LCM of 11,12 and 30?
4.What is the LCM of 17 and 11?
5.What is the LCM of 11 and 16?
Important glossaries for the LCM of 11 and 12
- Multiple: A number and any integer multiplied.
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers:Numbers that have no common factors other than 1.
- Fraction: A representation of 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.
