LCM Calculator
Find the Least Common Multiple (LCM) of numbers with simple steps.
What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM), sometimes called the Lowest Common Multiple, is the smallest positive integer that is divisible by each of the input numbers without leaving a remainder.
For example, for the numbers 4 and 6:
- Multiples of 4: 4, 8, 12, 16, 20, 24, ...
- Multiples of 6: 6, 12, 18, 24, 30, 36, ...
- Common Multiples: 12, 24, 36, ...
- Least Common Multiple: 12
Methods to Find LCM
1. Listing Multiples
List the multiples of each number until you find the first one that appears in all lists. This method is effective for small numbers.
2. Prime Factorization Method
Find the prime factorization of each number. The LCM is the product of the highest power of every prime factor present.
Example for 12 and 15:
- 12 = 2 × 2 × 3 = 2² × 3¹
- 15 = 3 × 5 = 3¹ × 5¹
- Highest powers: 2², 3¹, 5¹
- LCM = 4 × 3 × 5 = 60
3. Using GCD Formula
For two numbers a and b, you can use their Greatest Common Divisor (GCD):
LCM(a, b) = |a × b| / GCD(a, b)
Uses of LCM
- Fractions: Finding the Least Common Denominator (LCD) to add or subtract fractions.
- Scheduling: Determining when two repeating events will align (e.g., lights blinking at different intervals).
- Logistics: Aligning packaging and shipment quantities.
Frequently Asked Questions
Can LCM be smaller than the numbers?
No, the LCM must be greater than or equal to the largest of the input numbers.
What is the LCM of prime numbers?
The LCM of distinct prime numbers is simply their product.