The LCM in simple words
A multiple of a number is what you get when you count up in steps of that number. The multiples of 4 are 4, 8, 12, 16, 20 and so on.
The least common multiple (LCM) is the smallest number that is a multiple of all your numbers. In other words, it is the first number every one of them divides into exactly.
Example: the multiples of 4 are 4, 8, 12, 16 … and the multiples of 6 are 6, 12, 18 … The first number in both lists is 12, so the LCM of 4 and 6 is 12.
You use the LCM to add fractions with different bottom numbers. To add 1/4 and 1/6, write both over 12: 3/12 + 2/12 = 5/12.
How to find the least common multiple
Factor each input into primes. For each prime appearing anywhere in the list, keep its highest exponent; multiply those prime powers. This produces the smallest positive number divisible by all the inputs.
For two positive integers, LCM(a, b) = (a ÷ GCF(a, b)) × b. Apply that operation repeatedly for a longer list. The calculator checks safe integer precision rather than presenting a rounded large integer as exact.
Example: 12, 18 and 30
12 = 2² × 3, 18 = 2 × 3², and 30 = 2 × 3 × 5. Keeping the highest powers gives 2² × 3² × 5 = 180. Check the result: 180 ÷ 12 = 15, 180 ÷ 18 = 10, and 180 ÷ 30 = 6.
Common denominators and repeating events
An LCM supplies a common denominator when adding fractions. For events repeating every 12 and 18 days from the same starting point, the first shared repeat is after 36 days. If starting times differ, the LCM alone does not determine the next coincidence.
Enter 2–100 non-zero integers with magnitudes at most 10¹². Negative signs are ignored. Zero is excluded because this tool seeks a positive common multiple. Decimal or invalid entries cause the whole list to be rejected.
Least common denominator of fractions
Choose "LCD of fractions" and enter fractions, mixed numbers, whole numbers or decimals. The least common denominator is the LCM of the denominators. Each fraction is then rewritten over it by multiplying the numerator and denominator by LCD ÷ denominator.
Example: for 1/4, 5/6 and 2 1/3, first write 2 1/3 as 7/3. The denominators 4 = 2², 6 = 2 × 3 and 3 give an LCD of 2² × 3 = 12, so the fractions become 3/12, 10/12 and 28/12. If a fraction is not in lowest terms, reducing it first can give a smaller LCD, and the calculator shows that value too.