Least Common Multiple (LCM) of 199 and 122
The least common multiple (LCM) of 199 and 122 is 24278.
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 199 and 122?
First, calculate the GCD of 199 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 122 = 1 remainder 77 |
| 2 | 122 ÷ 77 = 1 remainder 45 |
| 3 | 77 ÷ 45 = 1 remainder 32 |
| 4 | 45 ÷ 32 = 1 remainder 13 |
| 5 | 32 ÷ 13 = 2 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 133 | 16492 |
| 151 and 21 | 3171 |
| 181 and 188 | 34028 |
| 108 and 170 | 9180 |
| 23 and 190 | 4370 |