Last updated on May 26th, 2025
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 12. 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 10 and 12 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 10 and 12 can be found using the following steps:
Steps:
1. Write down the multiples of each number
— Multiples of 10 = 10, 20, 30, 40, 50, 60, …
— Multiples of 12 = 12, 24, 36, 48, 60, …
2. Ascertain the smallest multiple from the listed multiples
— The smallest common multiple is 60.
Thus, LCM(10, 12) = 60.
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
1. Find the prime factors of the numbers:
— Prime factorization of 10 = 2 × 5
— Prime factorization of 12 = 2 × 2 × 3
2. Take the highest powers of each prime factor:
— Highest power of 2 = 2²
— Highest power of 3 = 3
— Highest power of 5 = 5
LCM(10, 12) = 2² × 3 × 5 = 60
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:
1. Write the numbers:
2. Divide by common prime factors and multiply the divisors:
— 2 × 2 × 3 × 5 = 60
Thus, LCM(10, 12) = 60.
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 10 and 12, make a note while practicing.
Bus A and bus B, run every 10 and 12 days, both leave the station today. When will they next leave the station on the same day again?
The LCM of 10 and 12 is 60
The buses will leave together next in 60 days. 60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.
In a neighborhood park, the fountain show is turned on every 10 minutes, and the light show every 12 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?
The LCM of 10 and 12 is 60.
Both the shows will turn on at the same time in 60 minutes,60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.
The sprinkler watering system waters every 10 days and the drip watering system waters every 12 days. On which day do they have to be turned on together?
The LCM of 10 and 12 is 60
Both the watering systems have to be turned on together in 60 days. 60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.
A car mechanic services a red car every 10 days and a blue car every 12 days. If the cars are serviced today, when will they be serviced next together?
The LCM of 10 and 12 is 60.
Both cars will be serviced again in 60 days.60 is the LCM of 10 and 12, expressing the smallest time interval between the digits.
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.