Least Common Multiple (LCM) of 114 and 192
The least common multiple (LCM) of 114 and 192 is 3648.
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 114 and 192?
First, calculate the GCD of 114 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 192 = 0 remainder 114 |
| 2 | 192 ÷ 114 = 1 remainder 78 |
| 3 | 114 ÷ 78 = 1 remainder 36 |
| 4 | 78 ÷ 36 = 2 remainder 6 |
| 5 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 51 | 10200 |
| 24 and 47 | 1128 |
| 72 and 30 | 360 |
| 117 and 158 | 18486 |
| 113 and 82 | 9266 |