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138 LearnersLast updated on November 29th, 2024
LCM of 8,9 and 10
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8,9 and 10. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. In our daily life, we use application of LCM for setting alarms in our clock or grouping any items.
What is the LCM of 8,9 and 10?
The LCM of 8,9 and 10 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 8,9 and 10?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 8,9 and 10 using the Listing multiples method
The LCM of 8,9 and 10 can be found using the following steps;
Step 1: Write down the multiples of each number:
Multiples of 8 = 8,16,24,32,…
Multiples of 9= 9,18,27,36,45,54,63,…
Multiples of 10 = 10,20,30,40,50,60,70,80,90,100,110,…
Step 2: Ascertain the smallest multiple from the listed multiples of 8 and 9.
The LCM of 8,9 and 10 =360
LCM of 8,9 and 10 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.
Step 1: Find the prime factors of the numbers:
Prime factorization of 8 = 2×2×2
Prime factorization of 9 = 3×3
Prime factorization of 10 = 2×5
Step 2: Multiply the highest power of each factor ascertained to get the LCM:
LCM (8,9) = 2×2×2×3×3×5 = 360
LCM of 8,9 and 10 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1: Write down the numbers in a row;
Step 2: 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.
Step 3: The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×2×2×3×3×5 = 360
LCM (8,9,10)=360
Common Mistakes and how to avoid them while finding the LCM of 8,9 and 10
LCM of 8,9 and 10 Examples
Problem 1
The LCM (8,9,x) is 360. Find x.
Explanation
Problem 2
One side of the triangular running track is 8 meters long, the second 9 meters long, and the third 10 meters long. What is the shortest length of a fence needed to enclose the track?
Explanation
Problem 3
a = 8, b=9, c=10, verify in LCM(a,b,c)×HCF(a,b,c) =a×b×c
Explanation
FAQ’s on LCM of 8 and 9 and 10
1.What is the HCF of 8,9 and 10?
2.List the common factors of 8,9,10,15.
3.What is the LCM of 8,10 and 15?
4.What is the LCM of 8,9 and 11?
5.What is the LCM of 8,9 and 12?
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.
