Least Common Multiple (LCM) of 198 and 164
The least common multiple (LCM) of 198 and 164 is 16236.
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 164?
First, calculate the GCD of 198 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 164 = 1 remainder 34 |
| 2 | 164 ÷ 34 = 4 remainder 28 |
| 3 | 34 ÷ 28 = 1 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 71 | 2698 |
| 167 and 161 | 26887 |
| 54 and 20 | 540 |
| 67 and 158 | 10586 |
| 75 and 109 | 8175 |