Least Common Multiple (LCM) of 122 and 192
The least common multiple (LCM) of 122 and 192 is 11712.
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 122 and 192?
First, calculate the GCD of 122 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 192 = 0 remainder 122 |
| 2 | 192 ÷ 122 = 1 remainder 70 |
| 3 | 122 ÷ 70 = 1 remainder 52 |
| 4 | 70 ÷ 52 = 1 remainder 18 |
| 5 | 52 ÷ 18 = 2 remainder 16 |
| 6 | 18 ÷ 16 = 1 remainder 2 |
| 7 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 45 | 1260 |
| 97 and 11 | 1067 |
| 195 and 47 | 9165 |
| 106 and 60 | 3180 |
| 98 and 23 | 2254 |