Least Common Multiple (LCM) of 177 and 197
The least common multiple (LCM) of 177 and 197 is 34869.
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 177 and 197?
First, calculate the GCD of 177 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 197 = 0 remainder 177 |
| 2 | 197 ÷ 177 = 1 remainder 20 |
| 3 | 177 ÷ 20 = 8 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 69 | 1311 |
| 65 and 191 | 12415 |
| 58 and 57 | 3306 |
| 105 and 120 | 840 |
| 16 and 106 | 848 |