Last updated on May 26th, 2025
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.
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.
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
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
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
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
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8,9 and 10 make a note while practicing.
The LCM (8,9,x) is 360. Find x.
To find x, we use the formula → LCM(a,b,c) = LCM(LCM(a,b),c)/HCF(a,b,c)
LCM (8,9)=72
But we already know that; LCM of 8,9, x = 360
The missing number must be 10:
LCM(72,10) = 360
the above is how we ascertain x, the third number.
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?
The LCM of 8,9 and 10 = 360
The smallest length that can be divided by both 8,9 and 10 can be divided by is 360. The shortest length of the fence is 360 meters.
a = 8, b=9, c=10, verify in LCM(a,b,c)×HCF(a,b,c) =a×b×c
LCM(a,b,c)×HCF(a,b,c) =a×b×c
HCF (8,9,10) = 1
LCM(8,9,10) = 360
LCM(a,b,c)×HCF(a,b,c) =a×b×c
360×1=8×9×10
360 is not equal to 720.
The formula is only valid when all prime factors are accounted for and the values for HCF and LCM are to be consistent.
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.
: She loves to read number jokes and games.