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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.
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:
A 24-by-60 rectangle is covered with ten 12-by-12 square tiles, where 12 is the GCD of 24 and 60. More generally, an a-by-b rectangle can be covered with square tiles of side length c only if c is a common divisor of a and b.
14, 49, −21 and 0 are multiples of 7, whereas 3 and −6 are not. This is because there are integers that 7 may be multiplied by to reach the values of 14, 49, 0 and −21, while there are no such integers for 3 and −6.
Equivalently, any two elements of R have a least common multiple (LCM). [ 1 ] A GCD domain generalizes a unique factorization domain (UFD) to a non- Noetherian setting in the following sense: an integral domain is a UFD if and only if it is a GCD domain satisfying the ascending chain condition on principal ideals (and in particular if it is ...
The least common multiple of a and b is equal to their product ab, i.e. lcm(a, b) = ab. [4] As a consequence of the third point, if a and b are coprime and br ≡ bs (mod a), then r ≡ s (mod a). [5] That is, we may "divide by b" when working modulo a.
A vessel claiming to be a Higgins LCM-3 is on display at the Battleship Cove maritime museum in Fall River, Massachusetts, however this vessel has the superstructure and overall length of an LCM-6. [5] Another Higgins LCM-3 is displayed at the Museo Storico Piana delle Orme in Province of Latina, Italy, 18 miles east of Anzio. [6]
The LCM-1E is a class of amphibious mechanized landing ... 12 additional units were ordered to service ... This allows them to operate up to 20 nautical miles (37 km ...