216 LearnersLast updated on May 26th, 2025
LCM of 7 and 12
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 7 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 7 and 12?
The LCM of 7 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.
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How to Find the LCM of 7 and 12?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 7 and 12 using the Listing Multiples Method
The LCM of 7 and 12 can be calculated using the following steps:
Steps:
- Write down the multiples of each number
— Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, …
— Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …
- Ascertain the smallest multiple from the listed multiples:
— The smallest common multiple is 84.
Thus, LCM(7, 12) = 84
LCM of 7 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:
- Prime factorization of 7 = 7 (since 7 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(7, 12) = 2² × 3 × 7 = 84
LCM of 7 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. Divide by common prime factors and multiply the divisors.
— 2 × 2 × 3 × 7 = 84
Thus, LCM(7, 12) = 84
Common Mistakes and how to avoid them while finding the LCM of 7 and 12
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 7 and 12, make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 7 and 12
This can be avoided by always double-checking the multiples of the numbers 7 and 12 and by not stopping too early. To elaborate, listing 7,14 as multiples of 7 and 12,24 as multiples of 12 and assuming 24 is the LCM.
Mistake 2
Confusing between LCM and HCF of the numbers 7 and 12
This can be avoided by learning that the LCM deals with multiples of the numbers 7 and 12, while HCF focuses on divisors of, 7 and 12 i.e., the HCF of 7 and 12 is 1, and the LCM is 84.
Mistake 3
Skipping the prime factors of the given numbers
Errors in prime factorization often include incorrectly factoring 7 and 12. To illustrate, factoring 12 as 34 instead of 3×4. Doing so will yield the wrong LCM.
Mistake 4
Multiplying the numbers directly
Incorrectly assuming that multiplying the numbers 7 and 12 and assuming the product is the LCM instead of finding the lowest multiple.
Mistake 5
Skipping the LCM in the list method
Oven, the first common multiples in the list of multiples are ignored due to an oversight, like 12 that appears on the list of both 7 and 12.
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LCM of 7 and 12 Examples
Problem 1
A movie theater alternates between a crime film and a children’s film. The crime film is shown every 7 days and the children’s film is shown every 12 days. In how many days will they both be screened together?
The LCM of 7 and 12 is 84.
Explanation
Both films will be shown on the same day again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.
Problem 2
An HP Printer prints a batch every 7 minutes and a Canon printer prints a batch every 12 minutes. If the machines start at 10:00 AM, when will they print out a batch at the same time?
The LCM of 7 and 12 is 84.
Explanation
Both machines will print a batch together at 11:24AM. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.
Problem 3
The sprinkler watering system waters every 7 days and the drip watering system waters every 12 days. On which day do they have to be turned on together?
The LCM of 7 and 12 is 84.
Explanation
Both the watering systems have to be turned on together in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.
Problem 4
An assembly is held every 7 days and a debate competition every 12 days. If both the events occur today, in how many days will they occur together again?
The LCM of 7 and 12 is 84.
Explanation
The events will occur together again in 84 days. The LCM of 7 and 12 is 84, which is the smallest common time interval between the digits.
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FAQs on LCM of 7 and 12
1.Why is the LCM of 7 and 12 not simply their product (7 Ă— 12 = 84) ?
2.How do you find the LCM with different bases in an exponential equation ?
3.What is the relationship between the Greatest Common Divisor (GCD)/ Highest Common Factor (HCF) and LCM of 7 and 12?
4.What are the factors of 7 and 12?
5.Find the LCM of 7 and 12 using the continuous division method.
6.How can children in United States use numbers in everyday life to understand LCM of 7 and 12?
7.What are some fun ways kids in United States can practice LCM of 7 and 12 with numbers?
8.What role do numbers and LCM of 7 and 12 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 7 and 12 skills?
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Important glossaries for the LCM of 7 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 or 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.
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