Least Common Multiple (LCM) of 120 and 198
The least common multiple (LCM) of 120 and 198 is 3960.
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 120 and 198?
First, calculate the GCD of 120 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 198 = 0 remainder 120 |
| 2 | 198 ÷ 120 = 1 remainder 78 |
| 3 | 120 ÷ 78 = 1 remainder 42 |
| 4 | 78 ÷ 42 = 1 remainder 36 |
| 5 | 42 ÷ 36 = 1 remainder 6 |
| 6 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 67 | 2211 |
| 156 and 86 | 6708 |
| 193 and 49 | 9457 |
| 84 and 68 | 1428 |
| 117 and 89 | 10413 |