Least Common Multiple (LCM) Calculator
Type two whole numbers and read the smallest number both divide into, with the working that gets you there rather than the answer on its own. The LCM is found through the greatest common factor, so this page shows Euclid's divisions and then the line that turns them into the multiple: for 252 and 198 the factor is 18, and 252 / 18 x 198 = 2,772. The factor stays on screen under the answer, since a common denominator usually needs both. Add boxes for a third number and a fourth and the multiple covers all of them, taken two at a time.
LCM of 252 and 1982,772GCF 18
Euclid
252 = 1 x 198 + 54 198 = 3 x 54 + 36 54 = 1 x 36 + 18 36 = 2 x 18 + 0 remainder 0, so the factor is 18 252 / 18 x 198 = 2,772
The least common multiple of 252 and 198 is 2,772. Their greatest common factor is 18, in 4 steps.
Whole numbers only, one to a box, or several in one box separated by spaces. Add a number for a third and a fourth: both answers then cover all of them.
Factor or multiple, and which one you want. The greatest common factor is the largest number that divides all of yours with nothing left over, so it is the one to divide by when you are reducing a fraction or splitting things into equal groups. The least common multiple is the smallest number they all divide into, which is what you need for a common denominator or for two repeating schedules that must line up. Multiples never run out, so there is no largest one to find and the least is the useful answer. Euclid’s algorithm gives both: divide the larger by the smaller, keep the remainder, repeat until the remainder is zero, and the last divisor is the factor. Then the multiple is the first number divided by that factor and multiplied by the second. The Euclidean algorithm on whole numbers, with every step shown, and exact past the usual safe-integer limit because it works in BigInt. It cannot take a decimal or a fraction, and it says so rather than rounding one for you.
Common questions
- What is the least common multiple?
- The smallest whole number that every number you gave divides into exactly. For 4 and 6 it is 12, because 12 is 4 times 3 and 6 times 2, and nothing smaller works. It is the number you need for a common denominator when adding fractions, and the number of days until two schedules that repeat every 4 and every 6 days land together again. Two numbers with nothing in common multiply: 17 and 23 give 391. When one number divides the other, the larger one is already the answer, so 12 and 36 give 36.
- How is the LCM worked out here?
- From the greatest common factor, which Euclid's algorithm finds first. Two numbers multiplied together equal their factor multiplied by their multiple, so the multiple is one number divided by the shared factor and then multiplied by the other. The pane shows every division on the way to the factor, then the closing line does the last piece in the order it is actually worked: 252 / 18 x 198 = 2,772. Dividing before multiplying is the honest order and keeps the intermediate numbers the size they should be. You can check the result: 2,772 is 252 times 11 and 198 times 14.
- How do I find the LCM of three or more numbers?
- Press Add a number and another box appears, up to ten of them. The multiple is folded two at a time: for 24, 30 and 72 the tool takes 24 and 30 to 120, then 120 and 72 to 360, and the closing line reads that the multiple of all 3 is 360. That is the same method you would use on paper, and it works in any order. The factor of the same three numbers, 6, is shown underneath at the same time.
- Is the LCM the same as the lowest common denominator?
- For adding fractions, yes: the lowest common denominator of two fractions is the least common multiple of their denominators. To add one seventh and one sixth, put 7 and 6 in the boxes, read 42, and rewrite them as six forty-seconds and seven forty-seconds. The greatest common factor is the number for the other direction, reducing a fraction once you have added it, which is why this page keeps it on screen beside the multiple.
- Can I put in decimals, fractions or very large numbers?
- Whole numbers only, and it says so rather than rounding: a decimal like 12.5 is refused by name, and a fraction is asked to be entered as its top and bottom separately. Large is fine. Everything runs in BigInt, up to 200 digits a number, so nothing rounds where an ordinary calculator would. One thing to watch: a comma separates one number from the next here, so write 1234 rather than 1,234.
- Where do I get the greatest common factor instead?
- It is already on this page, under the answer and in the readout, and the Lead with control swaps which of the two fills the stage. The main page opens with the factor leading and explains Euclid's algorithm in more detail. This page is the same tool opened on the multiple, so nothing is missing from either one.
The Euclidean algorithm on whole numbers, with every step shown, and exact past the usual safe-integer limit because it works in BigInt. It cannot take a decimal or a fraction, and it says so rather than rounding one for you.