Least Common Multiple (LCM) of 108 and 192
The least common multiple (LCM) of 108 and 192 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 108 and 192?
First, calculate the GCD of 108 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 192 = 0 remainder 108 |
| 2 | 192 ÷ 108 = 1 remainder 84 |
| 3 | 108 ÷ 84 = 1 remainder 24 |
| 4 | 84 ÷ 24 = 3 remainder 12 |
| 5 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 200 | 9800 |
| 25 and 13 | 325 |
| 86 and 18 | 774 |
| 78 and 70 | 2730 |
| 54 and 109 | 5886 |