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 |
|---|---|
| 164 and 83 | 13612 |
| 87 and 53 | 4611 |
| 76 and 182 | 6916 |
| 35 and 55 | 385 |
| 161 and 109 | 17549 |