Least Common Multiple (LCM) of 106 and 195
The least common multiple (LCM) of 106 and 195 is 20670.
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 106 and 195?
First, calculate the GCD of 106 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 195 = 0 remainder 106 |
| 2 | 195 ÷ 106 = 1 remainder 89 |
| 3 | 106 ÷ 89 = 1 remainder 17 |
| 4 | 89 ÷ 17 = 5 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 102 | 1632 |
| 107 and 172 | 18404 |
| 148 and 71 | 10508 |
| 166 and 133 | 22078 |
| 98 and 120 | 5880 |