Least Common Multiple (LCM) of 198 and 91
The least common multiple (LCM) of 198 and 91 is 18018.
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 91?
First, calculate the GCD of 198 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 91 = 2 remainder 16 |
| 2 | 91 ÷ 16 = 5 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 167 | 7181 |
| 182 and 133 | 3458 |
| 75 and 90 | 450 |
| 114 and 135 | 5130 |
| 59 and 45 | 2655 |