Least Common Multiple (LCM) of 195 and 164
The least common multiple (LCM) of 195 and 164 is 31980.
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 195 and 164?
First, calculate the GCD of 195 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 164 = 1 remainder 31 |
| 2 | 164 ÷ 31 = 5 remainder 9 |
| 3 | 31 ÷ 9 = 3 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 56 | 3752 |
| 95 and 28 | 2660 |
| 55 and 40 | 440 |
| 40 and 105 | 840 |
| 79 and 30 | 2370 |