300 LearnersLast updated on May 26th, 2025
LCM of 3, 4, and 5
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 9. 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 9?
The LCM of 3 and 9 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 3 and 9?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 3 and 9 using the Listing Multiples Method
The LCM of 3 and 9 can be found using the following steps:
Steps:
Write down the multiples of each number
— Multiples of 3 = 3, 6, 9, 12, 15, 18, …
— Multiples of 9 = 9, 18, 27, 36, …
Ascertain the smallest multiple from the listed multiples
— The least common multiple is 9.
LCM of 3 and 9 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 9 = 3 × 3
- Take the highest powers of each prime factor:
— Highest power of 3 = 3²
— Multiply the highest powers to get the LCM:
LCM(3, 9) = 3² = 9.
LCM of 3 and 9 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 find the LCM.
Steps:
— Write the numbers, divide by common prime factors and multiply the divisors.
— 3 × 3 = 9
Thus, LCM(3, 9) = 9.
Common Mistakes and how to avoid them while finding the LCM of 3 and 9
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 3 and 9
This can be avoided by always double-checking the multiples of the numbers 3 and 9 and by not stopping too early. To elaborate, listing 3,6 as multiples of 3 and 9,18 as multiples of 9 and assuming 6 is the LCM.
Mistake 2
Confusing between LCM and HCF of the numbers 3 and 9
This can be avoided by learning that the LCM deals with multiples of the numbers 3 and 9, while HCF focuses on divisors of, 3 and 9 i.e., the HCF of 3 and 9 is 3, and the LCM is 9.
Mistake 3
Skipping the prime factors of the given numbers
Errors in prime factorization often include incorrectly factoring 3 and 9. To illustrate, factoring 9 as 33 instead of 3×3. Doing so will yield the wrong LCM.
Mistake 4
Multiplying the numbers directly
Incorrectly assuming that multiplying the numbers 3 and 9 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 9 that appears on the list of both 3 and 9.
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LCM of 3 and 9 Examples
Problem 1
Runner A runs every 3 minutes in a trail and runner B every 9 minutes, and both of them start together. When will they both meet at the starting point again?
The LCM of 3 and 9 is 9.
Explanation
Runner A and B will meet at the starting point in 9 minutes, the LCM of 3 and 9 is 9, which is the smallest time interval between the digits.
Problem 2
Goods are received by a shipping company every 3 and 9 days. If the shipments have been received today, when will they next arrive at, the same day?
The LCM of 3 and 9 is 9.
Explanation
The goods will be received next in 9 days, the LCM of 3 and 9 is 9 which is the smallest time interval between the digits.
Problem 3
A yellow bulb is replaced every 3 months and a white bulb is replaced every 9 months. If both of them are replaced today, after how many months will they need to be replaced?
The LCM of 3 and 9 is 9.
Explanation
Both bulbs will need replacement together in 9 months. The LCM of 3 and 9 is 9 which is the smallest time interval between the digits.
Problem 4
The math teacher hands an assignment every 3 days and the science teacher every 9 days. If both the assignments are due today, when will the students be due to turn in their assignments next on the same day?
The LCM of 3 and 9 is 9.
Explanation
The math and science assignments will be due again in 9 days, the LCM is 9. The LCM of 3 and 9 is 9 which is the smallest time interval between the digits.
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FAQs on LCM of 3 and 9
1.Why is the LCM of 3 and 9 not simply their product (9 × 3 = 27) ?
2.How is the LCM of the algebraic expression 3x and 9x2 different from that of integers 3 and 9?
3.Can the LCM of two numbers ever be one of the numbers?
4.What is the LCM of 3,6,9 ?
5.What is the HCF of 3 and 9?
6.How can children in United States use numbers in everyday life to understand LCM of 3, 4, and 5?
7.What are some fun ways kids in United States can practice LCM of 3, 4, and 5 with numbers?
8.What role do numbers and LCM of 3, 4, and 5 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 3, 4, and 5 skills?
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Important glossaries for LCM of 3 and 9
- 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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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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