Least Common Multiple LCM Calculator
Calculator and example for calculating the least common multiple
The result of this function is the least common multiple (LCM) of the integers a and b.
To perform the calculation, enter the values for a and b, then click the 'Calculate' button.
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Description of the least common multiple
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the given numbers.
Example
This example shows how to determine the smallest common multiple of the numbers 18 and 30.
Determining multiples
\(V_{18} = \{18, 36, 54, 72, 90, 108, 126, 144, 162, 180, \dots\} \)
\(V_{30} = \{30, 60, 90, 120, 150, 180, 210, 240, \dots\} \)
The common multiples are marked.
\(V_{18} = \{18, 36, 54, 72, \underline{90}, 108, 126, 144, 162, \underline{180}, \dots\} \)
\(V_{30} = \{30, 60, \underline{90}, 120, 150, \underline{180}, 210, 240, \dots\} \)
Find and mark the least common multiple
\(V_{18} = \{18, 36, 54, 72, \color{blue}{\underline{90}}, 108, 126, 144, 162, \underline{180}, \dots\} \)
\(V_{30} = \{30, 60, \color{blue}{\underline{90}}, 120, 150, \underline{180}, 210, 240, \dots\} \)
Result of the function LCM
\( LCM(18, 30) = 90 \)
Calculation with the greatest common divisor (GCD)
For two numbers a and b:
\[LCM(a,b)=\frac{|a×b|}{GCD(a,b)}\]
where GCD is the greatest common divisor.
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