Least Common Multiple (LCM) of 192 and 122
The least common multiple (LCM) of 192 and 122 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 192 and 122?
First, calculate the GCD of 192 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 122 = 1 remainder 70 |
| 2 | 122 ÷ 70 = 1 remainder 52 |
| 3 | 70 ÷ 52 = 1 remainder 18 |
| 4 | 52 ÷ 18 = 2 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 65 | 7280 |
| 94 and 111 | 10434 |
| 121 and 67 | 8107 |
| 140 and 96 | 3360 |
| 68 and 180 | 3060 |