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145 LearnersLast updated on November 30th, 2024
LCM of 2 and 12
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 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 cars without understanding the rotation of wheel caused due to LCM.
What is the LCM of 2 and 12?
The LCM of 2 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 2 and 12?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 2 and 12 using the Listing Multiples Method
The LCM of 2 and 12 can be calculated using the following steps:
Step 1: Write down the multiples of each number
Multiples of 2 = 2,4,6,8,10,12,…
Multiples of 12 = 12, 24, 36, …
Step 2: Ascertain the smallest multiple from the listed multiples:
The smallest common multiple is 12.
Thus, LCM(2, 12) = 12.
LCM of 2 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: Find the prime factors of the numbers:
Prime factorization of 2 = 2
Prime factorization of 12 = 2 × 2 × 3
Step 2: Take the highest powers of each prime factor:
Highest power of 2 = 2²
Highest power of 2 = 2¹
Step 3:Multiply the highest powers to get the LCM:
LCM(2, 12) = 2² × 3 = 12.
LCM of 2 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; 2, 12 and divide by common prime factors and multiply the divisors.
Step 2: keep dividing untill we get 1 as remainder.
2 × 2 × 3 = 12
Thus, LCM(2, 12) = 12.
Common Mistakes and how to avoid them in LCM of 2 and 12
LCM of 2 and 12, examples
Problem 1
What percentage of the LCM of 2 and 12 is the smaller number (2)?
Explanation
Problem 2
What is the smallest number divisible by both 2 and 12?
Explanation
Problem 3
Two trains arrive at a station, one every 2 hours and the other every 12 hours. If both trains arrive at the station at the same time today, after how many hours will they arrive together again?
Explanation
FAQs on LCM of 2 and 12
1.What is the LCM of 2,12 and 20?
2.What are the factors of 2 and 12 ?
3.Which two numbers have the LCM of 12?
4.What is the LCM of 16 and 18?
5.What is the LCM of 2,8 and 12?
Important glossaries for the LCM of 2 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.
