Least Common Multiple Calculator
Find the Least Common Multiple (LCM) of two or more numbers. View the step-by-step solution using the prime factorization method.
Separate numbers with commas or spaces.
What is Least Common Multiple (LCM)?
The Least Common Multiple is the smallest positive integer that is evenly divisible by all the numbers in a given set. In other words, it is the smallest number that is a multiple of two or more numbers.
Example: LCM of 3 and 4 is 12, because 12 is the first number that both 3 and 4 can divide into without a remainder.
Methods to Find LCM
1. Prime Factorization (Used Here)
Break each number into its prime factors. The LCM is the product of the highest power of each prime factor found in the numbers.
2. Listing Multiples
List the multiples of each number until you find the first one they share.
Multiples of 3: 3, 6, 9, 12, 15...
Multiples of 4: 4, 8, 12, 16...
Smallest common is 12.
Real World Uses
- Adding Fractions: Finding the Lowest Common Denominator (LCD) to add fractions with different denominators.
- Scheduling: Calculating when two repeating events will happen at the same time (e.g., one bus arrives every 10 mins, another every 15 mins).
- Distribution: Determining the smallest number of items needed to split evenly into different sized groups.
? Frequently Asked Questions
Yes, when working with fractions. The Least Common Denominator (LCD) is simply the Least Common Multiple of the denominators.
No. The LCM must be greater than or equal to the largest number in the set. It is a 'multiple', so it grows upwards.
If the numbers are prime (like 3 and 5), the LCM is simply their product (3 × 5 = 15), because they share no common factors.