LCM in Excel: Shared Multiples, Cycles and Common Denominators

• Introduced: First introduction version is not established by the official history reviewed.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official LCM reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=LCM(number1,[number2],...)

Microsoft documents one required argument and 1–255 values in total. Noninteger values are truncated. Its dedicated page specifies #VALUE! for nonnumeric arguments, #NUM! for negative arguments, and #NUM! when the least common multiple reaches or exceeds 2^53.

The examples use positive integer counts. A zero interval does not describe a repeating positive cycle, and the zero-boundary native result is not established by the dedicated examples reviewed here. Do not extend the phrase smallest positive multiple into an unsupported zero-input guarantee.

For six, the first seven positive multiples are 6, 12, 18, 24, 30, 36, 42. For fourteen, they begin 14, 28, 42.

=LCM(6,14)

Expected result: 42. Multiplying the inputs gives 84, which is a shared multiple but not the least one because the inputs share a divisor of two.

For coprime inputs 5 and 7, the least common multiple is their product 35. That shortcut should not be generalized to inputs sharing factors.

=LCM(6,14,15)
=LCM(6.9,14.2)

Expected results are 210 and 42. The third interval must divide the result too, so 42 is no longer sufficient in the first formula. The second call uses truncated inputs 6 and 14 under the documented rule.

Fractional time intervals may instead need a carefully chosen smaller common unit. Truncating 6.9 minutes to six minutes changes the model, even though it is a documented numeric conversion.

Two fictional signals repeat every six and fourteen ticks and both occur at tick zero. Their next positive coincident tick is 42. After that they coincide at multiples of 42.

This conclusion depends on the common phase. If the second signal first occurs at tick three, LCM alone does not resolve the shifted schedule. A matching interval and a matching starting offset are different requirements.

The formula calculates an interval count; it does not account for calendars, time zones or skipped events. Keep those rules separate if adapting the example to a real timetable.

For 1/6 plus 1/14, the least common denominator is 42. The converted numerators are seven and three:

=LCM(6,14)
=42/6+42/14

Expected results are 42 and 10, representing 10/42. Reducing numerator and denominator by GCD(10,42)=2 gives 5/21. The decimal value is approximately 0.238095238.

GCD answers the reduction question, while LCM supplies the shared denominator. The two operations have complementary roles rather than interchangeable meanings.

For positive integers, =6/GCD(6,14)*14 has expected result 42. Dividing before multiplying avoids one unnecessarily larger intermediate in this small identity; it is not a blanket guarantee against native overflow or rounding.

The documented threshold is about the resulting LCM, unlike GCD’s stated parameter threshold. Large positive inputs can therefore have an invalid shared multiple even when each individual value appears reasonable. No exhaustive native extreme-value or type-coercion testing is claimed.

• Microsoft LCM reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.