Least Common Multiple (LCM) of 198 and 121
The least common multiple (LCM) of 198 and 121 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 198 and 121?
First, calculate the GCD of 198 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 121 = 1 remainder 77 |
| 2 | 121 ÷ 77 = 1 remainder 44 |
| 3 | 77 ÷ 44 = 1 remainder 33 |
| 4 | 44 ÷ 33 = 1 remainder 11 |
| 5 | 33 ÷ 11 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 189 | 2457 |
| 128 and 70 | 4480 |
| 53 and 135 | 7155 |
| 128 and 172 | 5504 |
| 23 and 108 | 2484 |