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188 LearnersLast updated on November 29th, 2024
LCM of 3 and 12
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 12. 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.
What is the LCM of 3 and 12?
The LCM of 3 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 3 and 12?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 3 and 12 using the Listing Multiples Method
The LCM of 2 and 5 can be calculated using the following steps:
Steps:
- Write down the multiples of each number
— Multiples of 3 = 3, 6, 9, 12, 15, 18, …
— Multiples of 12 = 12, 24, 36, …
- Ascertain the smallest multiple from the listed multiples:
— The smallest common multiple is 12.
Thus, LCM(3, 12) = 12
LCM of 3 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.
Steps:
- Find the prime factors of the numbers:
— Prime factorization of 3 = 3
— Prime factorization of 12 = 2 × 2 × 3
- Take the highest powers of each prime factor:
— Highest power of 2 = 2²
— Highest power of 3 = 3¹
- Multiply the highest powers to get the LCM:
—LCM(3, 12) = 2² × 3 = 12.
LCM of 3 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.
Steps:
- Write the numbers; 3, 12 and divide by common prime factors and multiply the divisors.
— 2 × 2 × 3 = 12
Thus, LCM(3, 12) = 12
Common Mistakes and how to avoid them while finding the LCM of 3 and 12
LCM of 3 and 12 Examples
Problem 1
Bus A and bus B, run every 3 and 12 days, both leave the station today. When will they next leave the station on the same day again?
Explanation
Problem 2
mployee A and employee B work different shifts. A works every 3 days, and B every 12 days. If they both work on the same day today, when will they next work together?
Explanation
Problem 3
Two trains arrive at a station, one every 3 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
Problem 4
Two clocks chime every 3 hours and 12 hours. If both the clocks chime together now, in how many hours will they chime next together?
Explanation
Problem 5
The product manager sends a reminder every 3 days for task A and 12 days for task B. On which day will the employees get both the mails?
Explanation
FAQs on LCM of 3 and 12
1.How do you find the LCM with different bases in an exponential equation?
2.What is the LCM formula using the HCF?
3.Why is the LCM of 2 and 5 not simply their product (3 × 12 = 36)?
4.How to find the LCM of numbers 3 and 12 quickly ?
5.What is the LCM of 3,4,12?
Important glossaries for the LCM of 3 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.
