LCM LCM Calculator (Least Common Multiple)

LCM Result

What is LCM (Least Common Multiple)?

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by two or more given numbers.

LCM(4, 6) = 12
Because 12 is the smallest number divisible by both 4 and 6.

Relationship Between LCM and GCD

LCM(a, b) = (a × b) / GCD(a, b)

LCM Applications

  • Adding and subtracting fractions with different denominators
  • Scheduling problems (when two events coincide)
  • Finding patterns in number sequences

LCM Calculation Methods

Method 1: Listing Multiples

LCM(4, 6):
Multiples of 4: 4, 8, 12, 16, 20, 24...
Multiples of 6: 6, 12, 18, 24...
First common = 12

Method 2: Prime Factorization (most reliable)

LCM(12, 18):
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 4 × 9 = 36
(Take highest power of each prime factor)

Method 3: Using GCD (fastest for two numbers)

LCM(a,b) = (a × b) / GCD(a,b)
LCM(12, 18) = (12 × 18) / GCD(12,18) = 216 / 6 = 36

LCM Reference Table

NumbersGCDLCM
4, 6212
8, 12424
15, 20560
7, 11177
6, 9, 12336

Real-World Applications

  • Adding fractions: 1/4 + 1/6 → LCM(4,6)=12 → 3/12 + 2/12 = 5/12
  • Scheduling: Bus A runs every 8 min, Bus B every 12 min — they coincide every LCM(8,12)=24 minutes
  • Gear ratios: Gears with different tooth counts return to the same position after LCM rotations
  • Music: Finding when rhythmic patterns of different lengths coincide (polyrhythm)

LCM in Music Theory

LCM has a beautiful application in music — it tells you when different rhythmic patterns will sync up again:

Pattern A repeats every 4 beats, Pattern B every 6 beats
LCM(4, 6) = 12
They sync up every 12 beats — a polyrhythm

This is why many musical time signatures and polyrhythms are based on LCM relationships. A 3-against-4 polyrhythm (LCM=12) creates the characteristic "feel" of much African and Latin music.

LCM for Multiple Fractions

When adding three or more fractions, find the LCM of all denominators:

1/4 + 1/6 + 1/8
LCM(4, 6, 8) = 24
= 6/24 + 4/24 + 3/24 = 13/24

LCM vs GCD — The Relationship

For any two numbers a and b:
LCM(a, b) × GCD(a, b) = a × b
Example: LCM(12,18)=36, GCD(12,18)=6
36 × 6 = 216 = 12 × 18 ✓

Frequently Asked Questions

What is LCM of 4 and 6? ▼
LCM(4, 6) = 12. Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... The first common multiple is 12.
What is LCM of 12 and 18? ▼
LCM(12, 18) = 36. Using the formula: LCM = (12 × 18) / GCD(12, 18) = 216 / 6 = 36.
How is LCM used in fractions? ▼
LCM is used to find the common denominator when adding or subtracting fractions. For example, to add 1/4 + 1/6, find LCM(4,6) = 12, then convert: 3/12 + 2/12 = 5/12.