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A multiple of a natural (positive integral) number a is a natural number that is divisible by a without a remainder. Thus 156 is a multiple of 13, while 108 is not. A number n that is divisible by each of the numbers a, b, . . . ,m is called a common multiple of these numbers. Of all the common multiples of two or more numbers, one (not equal to zero) is the smallest, or least common multiple, and the others will be multiples of this number.
A number of problems in arithmetic reduce to finding the least common multiple of two or more numbers. In order to find the least common multiple of several numbers, we must first find the least common multiple of the first two numbers, then the least common multiple of that number and of the third number, and so on. If we know the greatest common divisior d of two numbers a and b, we may find their least common multiple m using the formula m =ab/d. Numbers that are multiples of 2 are called even, the other numbers being called odd.