Least Common Multiple (LCM) of 195 and 109
The least common multiple (LCM) of 195 and 109 is 21255.
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 109?
First, calculate the GCD of 195 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 109 = 1 remainder 86 |
| 2 | 109 ÷ 86 = 1 remainder 23 |
| 3 | 86 ÷ 23 = 3 remainder 17 |
| 4 | 23 ÷ 17 = 1 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 135 | 7560 |
| 69 and 93 | 2139 |
| 191 and 181 | 34571 |
| 11 and 194 | 2134 |
| 192 and 195 | 12480 |