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Common multiple calculator

Enter a list of integers to see their first positive common multiples. If any input is zero, zero is the only shared multiple.

Calculator

Least common multiple
60
Common multiples
IndexExact integer value
1.0000000060
2.00000000120
3.00000000180
4.00000000240
5.00000000300
6.00000000360
7.00000000420
8.00000000480
9.00000000540
10.00000000600

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How this calculator works

The least common multiple is the smallest positive integer divisible by every non-zero input. Combining the inputs one at a time with their greatest common divisor finds it. All subsequent positive common multiples are integer multiples of that least value. The tool uses exact integer arithmetic after validating each input, so a result may be longer than the ordinary numeric safe range. Negative signs do not affect the list.

Formula

lcm(a,b)=|a/gcd(a,b) × b|. For a non-zero list with least common multiple L, the positive common multiples are L, 2L, 3L, ... .

Worked example

For 4, 6 and 10, the least common multiple is 60. The first three positive shared multiples are 60, 120 and 180. For 3 and 5 they are 15, 30 and 45.

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Frequently asked questions

Why stop at fifty results?

There are infinitely many positive common multiples of non-zero integers. A finite prefix makes the pattern visible without generating an unbounded table.

What happens when an input is zero?

The only multiple of zero is zero. Consequently the only common multiple is zero, and the table contains that single value.

How many inputs are supported?

Enter two to fifteen integers. Each must be exactly representable as an ordinary safe integer; the resulting common multiples can be much larger.

Sources

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