Least Common Multiple (LCM) of 164 and 197
The least common multiple (LCM) of 164 and 197 is 32308.
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 197?
First, calculate the GCD of 164 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 197 = 0 remainder 164 |
| 2 | 197 ÷ 164 = 1 remainder 33 |
| 3 | 164 ÷ 33 = 4 remainder 32 |
| 4 | 33 ÷ 32 = 1 remainder 1 |
| 5 | 32 ÷ 1 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 15 | 270 |
| 125 and 172 | 21500 |
| 142 and 152 | 10792 |
| 174 and 79 | 13746 |
| 41 and 194 | 7954 |