Least Common Multiple (LCM) of 192 and 108
The least common multiple (LCM) of 192 and 108 is 1728.
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 192 and 108?
First, calculate the GCD of 192 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 108 = 1 remainder 84 |
| 2 | 108 ÷ 84 = 1 remainder 24 |
| 3 | 84 ÷ 24 = 3 remainder 12 |
| 4 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 11 | 1705 |
| 86 and 173 | 14878 |
| 117 and 177 | 6903 |
| 149 and 177 | 26373 |
| 120 and 56 | 840 |