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224 LearnersLast updated on November 29th, 2024
LCM of 8 and 9
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8 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 8 and 9?
The LCM of 8 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 8 and 9?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 8 and 9 using the Listing multiples method
The LCM of 8 and 9 can be found using the following steps;
Steps:
1. Write down the multiples of each number:
Multiples of 8 = 8,16,24,32,40,48,56,64,72…
Multiples of 9= 9,18,27,36,45,54,63,72…
2. Ascertain the smallest multiple from the listed multiples of 8 and 9.
The LCM of 8 and 9 = 72
LCM of 8 and 9 using the Prime Factorization
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 8 = 2×2×2
Prime factorization of 9 = 3×3
- Multiply the highest power of each factor ascertained to get the LCM:
LCM (8,9) = 2×2×2×3×3 = 72
LCM of 8 and 9 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
- Write down the numbers in a row;
- A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
- The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×2×2×3×3 = 72
LCM (8,9)=72
Common Mistakes and how to avoid them while finding the LCM of 8 and 9
LCM of 8 and 9 Examples
Problem 1
1. Bells at a High School ring for the assembly, 8 and 9 minutes apart, respectively. If they ring together at 1:00 PM, when will they ring together again?
Explanation
Problem 2
A running track is 8 meters long and 9 meters wide. What is the shortest length of a fence needed to enclose the track?
Explanation
Problem 3
One cookie jar is filled every 8 hours, and the candy jar is filled every 9 hours. If the jars started filling at the same time, how long will it take for the both of them to be filled?
Explanation
Problem 4
Two vans arrive at a store every 8 and 9 days, respectively, for a delivery. If they both arrive at the station today, when will they arrive together again?
Explanation
FAQ’s on LCM of 8 and 9
1.Why is the LCM of 8 and 9 not simply their product (8 × 9 = 72) ?
2.. What is the LCM of 8,9,10?
3.What is the relationship between the Highest common factor (HCF) and LCM of 8 and 9?
4.What is the HCF of 8 and 9?
5.What is the LCM of 8,9,11?
Important glossaries for the LCM of 8 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.
