Least Common Multiple (LCM) of 108 and 144
The least common multiple (LCM) of 108 and 144 is 432.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 108 and 144?
First, calculate the GCD of 108 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 144 = 0 remainder 108 |
| 2 | 144 ÷ 108 = 1 remainder 36 |
| 3 | 108 ÷ 36 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 60 | 5340 |
| 99 and 41 | 4059 |
| 119 and 23 | 2737 |
| 159 and 194 | 30846 |
| 84 and 13 | 1092 |