LCM
Returns the least common multiple of two or more integers. The LCM is the smallest positive integer that is divisible by all given numbers.
LCM(number1, [number2], ...)Arguments
number1First integernumber2Additional integers(optional)
=LCM(4, 6)12 is the smallest number divisible by both 4 and 6
=LCM(3, 5, 7)105 is divisible by 3, 5, and 7
=LCM(12, 18)36 is the smallest common multiple of 12 and 18
- •Useful for finding common denominators
- •Decimals are truncated before calculation
- •LCM(a,b) = (a * b) / GCD(a,b)
- •Passing a negative number to LCM, which returns a #NUM! error since the least common multiple is only defined for non-negative integers
- •Passing a non-integer number expecting an error - LCM actually truncates decimal values first, so LCM(4.9,6) calculates the LCM of 4 and 6
- •Confusing LCM with GCD - LCM finds the smallest number that all the inputs divide evenly into, while GCD finds the largest number that divides evenly into all the inputs, and the two produce very different results for the same inputs
GCDCalculates the greatest common divisor, essentially the inverse relationship to LCM's least common multiple.MODOften used alongside LCM when working with divisibility, like finding a common cycle length between repeating events.QUOTIENTSometimes combined with LCM in calculations involving fraction addition, where a common denominator is needed.Why does LCM return a #NUM! error?
One of the numbers supplied is negative - LCM only works with non-negative integers.
What's the difference between LCM and GCD?
LCM finds the smallest number that all the inputs evenly divide into, while GCD finds the largest number that evenly divides all the inputs - they answer opposite questions about the same set of numbers.
When is LCM useful in practice?
It's commonly used to find a common denominator when adding fractions, or to determine when repeating cycles (like schedules or intervals) will align again.
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