Last updated on May 26th, 2025
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.
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.
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
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
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
Prime factorization of 8 = 2×2×2
Prime factorization of 9 = 3×3
LCM (8,9) = 2×2×2×3×3 = 72
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
2×2×2×3×3 = 72
LCM (8,9)=72
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8 and 9 make a note while practicing.
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?
The LCM of 8 and 9 is 72.
The bells will ring together at 2:12 PM next. The LCM of the given digits is the smallest common multiple using which we ascertain the time asked.
A running track is 8 meters long and 9 meters wide. What is the shortest length of a fence needed to enclose the track?
The LCM of 8 and 9 is 72.
The smallest length that can be divided by both 8 and 9 can be divided by is 72. The shortest length of the fence is 72 meters.
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?
The LCM of 8 and 9 is 72.
Therefore, both jars will be filled at the same time again in 72 hours. The LCM (72) of the given digits is the smallest common multiple using which we ascertain the time asked.
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?
The LCM of 8 and 9 is 72.
The vans will arrive at the station together again in 72 days. The LCM of 8 and 9 is 72, is the smallest common multiple using which we ascertain the time asked.
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.