Find the lowest common multiple of two or more numbers — the smallest number that all of them divide evenly into.
The greatest common divisor of the pair is found first, using the Euclidean algorithm.
The product of the two numbers is divided by that GCD.
Dividing before multiplying keeps the intermediate numbers small and avoids overflow on large inputs.
LCM: |a × b| ÷ GCD(a, b)
For a list: Apply the same rule across the numbers in turn
Finding the LCM of 4 and 6.
Numbers: 4, 6
GCD of 4 and 6 is 2
Multiply: 4 × 6 = 24
Divide by the GCD: 24 ÷ 2 = 12
Answer: LCM = 12
Where is the LCM actually used?
Most often, it is used for adding fractions, where the lowest common denominator is the LCM of the bottom numbers. It also helps with timing questions — two buses leaving every 4 and 6 minutes will leave together again every 12 minutes.
Is the LCM always the two numbers multiplied together?
Only when they are coprime (share no common factor). 7 and 13 share no factors, so their LCM is 91. But 4 and 6 share a factor of 2, so their LCM is 12, not 24.