Least Common Multiple (LCM) of 19 and 195
The least common multiple (LCM) of 19 and 195 is 3705.
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 19 and 195?
First, calculate the GCD of 19 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 195 = 0 remainder 19 |
| 2 | 195 ÷ 19 = 10 remainder 5 |
| 3 | 19 ÷ 5 = 3 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 75 | 3900 |
| 127 and 150 | 19050 |
| 145 and 96 | 13920 |
| 66 and 11 | 66 |
| 70 and 165 | 2310 |