Least Common Multiple (LCM) of 77 and 195
The least common multiple (LCM) of 77 and 195 is 15015.
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 77 and 195?
First, calculate the GCD of 77 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 195 = 0 remainder 77 |
| 2 | 195 ÷ 77 = 2 remainder 41 |
| 3 | 77 ÷ 41 = 1 remainder 36 |
| 4 | 41 ÷ 36 = 1 remainder 5 |
| 5 | 36 ÷ 5 = 7 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 55 | 10835 |
| 67 and 75 | 5025 |
| 51 and 67 | 3417 |
| 120 and 118 | 7080 |
| 17 and 199 | 3383 |