Least Common Multiple (LCM) of 195 and 106
The least common multiple (LCM) of 195 and 106 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 195 and 106?
First, calculate the GCD of 195 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 106 = 1 remainder 89 |
| 2 | 106 ÷ 89 = 1 remainder 17 |
| 3 | 89 ÷ 17 = 5 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 53 | 9275 |
| 131 and 13 | 1703 |
| 57 and 147 | 2793 |
| 142 and 83 | 11786 |
| 52 and 80 | 1040 |