Least Common Multiple (LCM) of 164 and 198
The least common multiple (LCM) of 164 and 198 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 164 and 198?
First, calculate the GCD of 164 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 198 = 0 remainder 164 |
| 2 | 198 ÷ 164 = 1 remainder 34 |
| 3 | 164 ÷ 34 = 4 remainder 28 |
| 4 | 34 ÷ 28 = 1 remainder 6 |
| 5 | 28 ÷ 6 = 4 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 130 | 1430 |
| 199 and 125 | 24875 |
| 109 and 84 | 9156 |
| 132 and 17 | 2244 |
| 162 and 78 | 2106 |