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693 is the lowest common multiple of 7, 9, and 11. Multiplying 693 by 5 gives 3465, the smallest positive integer divisible by 3, 5, 7, 9, and 11. [1] 693 is a palindrome in bases 32, 62, 76, 98, 230, and 692. It is also a palindrome in binary: 1010110101. The reciprocal of 693 has a period of six: 1 / 693 = 0. 001443.
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. In general, two elements in a commutative ring can have no least common multiple or more than one. However, any two least common multiples of the same pair of elements are associates. [10]
gcd(a, b) is closely related to the least common multiple lcm(a, b): we have gcd(a, b)⋅lcm(a, b) = | a⋅b |. This formula is often used to compute least common multiples: one first computes the GCD with Euclid's algorithm and then divides the product of the given numbers by their GCD. The following versions of distributivity hold true:
The numbers 8 and 9 are coprime, despite the fact that neither—considered individually—is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition.
Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers:
In mathematics, a multiple is the product of any quantity and an integer. [1] In other words, for the quantities a and b , it can be said that b is a multiple of a if b = na for some integer n , which is called the multiplier .
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Least common multiple; Lowest common denominator This page was last edited on 5 February 2012, at 02:07 (UTC). Text is available under the Creative Commons ...