In a unique factorization domain, any two elements have a least common multiple.
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They had discovered the least common multiple for themselves, and they had used music to do it.
From the scientistatwork.blogs.nytimes.com
In general, two elements in a commutative ring can have no least common multiple or more than one.
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Once the prime factorizations of two numbers are known, their greatest common divisor and least common multiple can be found quickly.
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The least upper bound of two numbers is the smallest number that is divided by both of them, i.e. the least common multiple of the numbers.
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A least common multiple of a and b is a common multiple that is minimal in the sense that for any other common multiple n of a and b, m divides n.
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The problem is solved by the scribe to multiply the entire problem by a least common multiple of the denominators, solving the problem and then turning the values back into fractions.
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Given a positive integer n, the set of all positive divisors of n forms a distributive lattice, again with the greatest common divisor as meet and the least common multiple as join.
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For multiple reasons, the flu shot is one of the least effective vaccines in common use.