Least Common Multiple (LCM) of 121 and 198
The least common multiple (LCM) of 121 and 198 is 2178.
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 198?
First, calculate the GCD of 121 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 198 = 0 remainder 121 |
| 2 | 198 ÷ 121 = 1 remainder 77 |
| 3 | 121 ÷ 77 = 1 remainder 44 |
| 4 | 77 ÷ 44 = 1 remainder 33 |
| 5 | 44 ÷ 33 = 1 remainder 11 |
| 6 | 33 ÷ 11 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 35 | 4515 |
| 51 and 159 | 2703 |
| 178 and 142 | 12638 |
| 40 and 156 | 1560 |
| 78 and 180 | 2340 |