287 LearnersLast updated on May 26th, 2025
LCM of 12 and 18
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 12 and 18. 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 12 and 18?
The LCM of 12 and 18 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 12 and 18?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 12 and 18 using the Listing Multiples Method
The LCM of 12 and 18 can be found using the following steps:
Steps:
- List the multiples of each number
— Multiples of 12 = 12, 24, 36, 48, 60, 72, …
— Multiples of 18 = 18, 36, 54, 72, 90, …
- Figure the smallest multiple from the listed multiples
— The smallest common multiple is 36.
Thus, LCM(12, 18) = 36
LCM of 12 and 18 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:
- Devise prime factors of the given numbers:
— Prime factorization of 12 = 2 × 2 × 3
— Prime factorization of 18 = 2 × 3 × 3
- Pick the highest powers of each prime factor:
— Highest power of 2 = 2²
— Highest power of 3 = 3²
- Find the product of the highest powers to get the LCM:
LCM(12, 18) = 2² × 3² = 36.
LCM of 12 and 18 using the Division Method
This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to get the LCM.
Steps:
- Write the numbers:
- Divide by common prime factors and multiply the divisors:
— 2 × 2 × 3 × 3 = 36
Thus, LCM(12, 18) = 36.
Common Mistakes and how to avoid them while finding the LCM of 12 and 18
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3 and 9, make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 12 and 18.
This can be avoided by always double-checking the multiples of the numbers 12 and 18 and by not stopping too early. To elaborate, listing 12,24 as multiples of 12 and 18,36 as multiples of 18 and assuming 24 is the LCM.
LCM of 12 and 18 examples
Problem 1
Goods are received by a shipping company every 12 and 18 days. If the shipments have been received today, when will they next arrive at, the same day?
The LCM of 12 and 18 is 36.
Explanation
The goods will be received next in 36 days. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.
Problem 2
A maintenance schedule for projectors is set up every 12 weeks and 18 weeks at a school. If both the projectors are serviced today, in how many weeks will they be serviced again on the same day?
The LCM of 12 and 18 is 36.
Explanation
Both projectors will need maintenance again in 36 weeks.36 is the LCM of 12 and 18, which is the smallest time interval between the digits.
Problem 3
Two clocks strike every 12 hours and 18 hours. If both of them strike now, when will they next strike together?
The LCM of 12 and 18 is 36.
Explanation
Both clocks will chime together again in 36 hours. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.
Problem 4
In a neighborhood park, the fountain show is turned on every 12 minutes, and the light show every 18 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?
The LCM of 12 and 18 is 36.
Explanation
Both the shows will turn on at the same time in 36 minutes, 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.
Problem 5
A car mechanic services a red car every 12 days and a blue car every 18 days. If the cars are serviced today, when will they be serviced next together?
The LCM of 12 and 18 is 36.
Explanation
Both cars will be serviced again in 36 days. 36 is the LCM of 12 and 18, which is the smallest time interval between the digits.
FAQs on LCM of 12 and 18
1.Why is the LCM of 12 and 18 not simply their product (12 × 18 = 216)?
2.How do you find the LCM of 12 and 18 using a Venn diagram?
3.What is the LCM formula using the HCF?
4.If both the numbers are prime, what is the LCM? Explain in the case of 12 and 18.Â
5.How can you check if the LCM you ascertained is right? Explain using the digits 12 and 18.
6.How can children in Thailand use numbers in everyday life to understand LCM of 12 and 18?
7.What are some fun ways kids in Thailand can practice LCM of 12 and 18 with numbers?
8.What role do numbers and LCM of 12 and 18 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve LCM of 12 and 18 skills?
Important glossaries for the LCM of 12 and 18
- 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
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