LCM calculator
Find the least common multiple of 2 to 6 integers.
What this calculator covers
Use this calculator when you need a common multiple for denominator work, cycle matching, or grouped interval checks.
The pairwise reduction keeps the product-over-GCF logic visible, which is usually the fastest way to audit an LCM result by hand.
Frequently asked questions
- What is the least common multiple used for?
- The LCM is most commonly used to find a common denominator when adding or subtracting fractions. It also appears in scheduling problems where you need to find when repeating cycles — like two machines running on different intervals — will next align.
- How does the pairwise method work for more than two numbers?
- The calculator finds the LCM of the first two numbers, then treats that result as the new first number and finds the LCM with the third number, and so on. Repeating this chain across all inputs produces the same final answer as checking all numbers at once.
- What is the relationship between LCM and GCF?
- For any two positive integers, LCM(a, b) × GCF(a, b) = a × b. This means you can always find one from the other if you know the product of the two numbers and either the LCM or GCF.
- Can the LCM ever be smaller than any of the input numbers?
- No. The LCM is always greater than or equal to the largest number in the set, because it must be a multiple of every input.
Tool
Run the calculation
Result
RESULT · LCM
â„–153
Primary result
60
The least common multiple of 4, 6, 15 is 60.
- Values used
- 4, 6, 15
- Pairwise reduction
- lcm(4, 6) = |4 x 6| / 2 = 12 -> lcm(12, 15) = |12 x 15| / 3 = 60
- Least common multiple
- 60
Step-by-step solution
- 1.List the integers 4, 6, 15.
- 2.Reduce them pairwise using lcm(a, b) = |a x b| / gcd(a, b).
- 3.Carry the pairwise result forward until the final common multiple is 60.
Walkthrough
Visual walkthrough
LCM grows a common denominator by combining two integers at a time and dividing away the overlap counted twice.
01
Collect the integers
4, 6, 15
LCM uses positive whole numbers because it measures the first shared multiple of the selected integer set.
02
Combine two values at a time
lcm(a, b) = |a x b| / gcd(a, b)
Dividing by the GCF removes the duplicate shared factors that would otherwise be counted twice.
03
Carry the running multiple forward
60
Repeating the pairwise reduction across the full list yields the least shared multiple.
60