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In arithmetic and number theory, the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b. Since it is a multiple, it can be divided by a and b without a remainder. If there is no such positive integer, e.g., if a = 0 or b = 0, then lcm(a, b) is defined to be zero.) For example, the least common multiple of the numbers 4 and 6 is 12. When adding or subtracting vulgar fractions, it is useful to find the least common multiple of the denominators, often called the lowest common denominator. For instance, : where the denominator 42 was used because lcm(21, 6) = 42.

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Q: The definition of Common multiples
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