Least Common Multiple (LCM) of 109 and 195
The least common multiple (LCM) of 109 and 195 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 109 and 195?
First, calculate the GCD of 109 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 195 = 0 remainder 109 |
| 2 | 195 ÷ 109 = 1 remainder 86 |
| 3 | 109 ÷ 86 = 1 remainder 23 |
| 4 | 86 ÷ 23 = 3 remainder 17 |
| 5 | 23 ÷ 17 = 1 remainder 6 |
| 6 | 17 ÷ 6 = 2 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 120 | 360 |
| 161 and 194 | 31234 |
| 14 and 134 | 938 |
| 115 and 140 | 3220 |
| 30 and 95 | 570 |