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203 LearnersLast updated on December 2nd, 2024
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.
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
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
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?
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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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.
