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 |
|---|---|
| 130 and 174 | 11310 |
| 168 and 21 | 168 |
| 30 and 182 | 2730 |
| 85 and 113 | 9605 |
| 57 and 141 | 2679 |