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142 LearnersLast updated on November 29th, 2024
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.
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
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
FAQs on LCM of 7 and 12
1.Why is the LCM of 7 and 12 not simply their product (7 × 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.
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.
Fun Fact
: She loves to read number jokes and games.
