Least Common Multiple (LCM) of 121 and 199
The least common multiple (LCM) of 121 and 199 is 24079.
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 121 and 199?
First, calculate the GCD of 121 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 199 = 0 remainder 121 |
| 2 | 199 ÷ 121 = 1 remainder 78 |
| 3 | 121 ÷ 78 = 1 remainder 43 |
| 4 | 78 ÷ 43 = 1 remainder 35 |
| 5 | 43 ÷ 35 = 1 remainder 8 |
| 6 | 35 ÷ 8 = 4 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 105 | 105 |
| 20 and 59 | 1180 |
| 11 and 196 | 2156 |
| 21 and 87 | 609 |
| 61 and 142 | 8662 |