Least Common Multiple (LCM) of 164 and 195
The least common multiple (LCM) of 164 and 195 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 164 and 195?
First, calculate the GCD of 164 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 195 = 0 remainder 164 |
| 2 | 195 ÷ 164 = 1 remainder 31 |
| 3 | 164 ÷ 31 = 5 remainder 9 |
| 4 | 31 ÷ 9 = 3 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 111 | 3885 |
| 89 and 31 | 2759 |
| 185 and 146 | 27010 |
| 78 and 114 | 1482 |
| 93 and 71 | 6603 |