The least common multiple of two integers is the smallest positive integer between all the multiples of both. It is usually written as LCM(a, b).[1] Likewise, the LCM of more than two integers is the smallest positive integer that is divisible by each of them.[2][3]
Overview
Elementary arithmetic
In elementary arithmetic, the LCM is also the "lowest common denominator" (LCD) that must be calculated, before fractions can be added, subtracted or compared.
A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of 5 and 2 as well.
Relations with the greatest common divisor
It is known that:
where is the greatest common divisor of a and b, This formula is often used to compute the LCD, by first finding the GCD of a and b.
Related pages
References
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