Least Common Multiple (LCM) of 195 and 77
The least common multiple (LCM) of 195 and 77 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 195 and 77?
First, calculate the GCD of 195 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 77 = 2 remainder 41 |
| 2 | 77 ÷ 41 = 1 remainder 36 |
| 3 | 41 ÷ 36 = 1 remainder 5 |
| 4 | 36 ÷ 5 = 7 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 195 | 5655 |
| 185 and 120 | 4440 |
| 179 and 106 | 18974 |
| 93 and 62 | 186 |
| 151 and 85 | 12835 |