Least Common Multiple (LCM) of 122 and 199
The least common multiple (LCM) of 122 and 199 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 122 and 199?
First, calculate the GCD of 122 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 199 = 0 remainder 122 |
| 2 | 199 ÷ 122 = 1 remainder 77 |
| 3 | 122 ÷ 77 = 1 remainder 45 |
| 4 | 77 ÷ 45 = 1 remainder 32 |
| 5 | 45 ÷ 32 = 1 remainder 13 |
| 6 | 32 ÷ 13 = 2 remainder 6 |
| 7 | 13 ÷ 6 = 2 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 114 | 11058 |
| 42 and 175 | 1050 |
| 89 and 90 | 8010 |
| 25 and 116 | 2900 |
| 137 and 41 | 5617 |