Least Common Multiple (LCM) of 197 and 77
The least common multiple (LCM) of 197 and 77 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 197 and 77?
First, calculate the GCD of 197 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 77 = 2 remainder 43 |
| 2 | 77 ÷ 43 = 1 remainder 34 |
| 3 | 43 ÷ 34 = 1 remainder 9 |
| 4 | 34 ÷ 9 = 3 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 88 | 5720 |
| 129 and 195 | 8385 |
| 186 and 69 | 4278 |
| 170 and 188 | 15980 |
| 164 and 164 | 164 |