Least Common Multiple (LCM) of 77 and 197
The least common multiple (LCM) of 77 and 197 is 15169.
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 197?
First, calculate the GCD of 77 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 197 = 0 remainder 77 |
| 2 | 197 ÷ 77 = 2 remainder 43 |
| 3 | 77 ÷ 43 = 1 remainder 34 |
| 4 | 43 ÷ 34 = 1 remainder 9 |
| 5 | 34 ÷ 9 = 3 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 129 | 23865 |
| 143 and 144 | 20592 |
| 174 and 39 | 2262 |
| 162 and 26 | 2106 |
| 127 and 70 | 8890 |