Least Common Multiple (LCM) of 177 and 122
The least common multiple (LCM) of 177 and 122 is 21594.
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 122?
First, calculate the GCD of 177 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 122 = 1 remainder 55 |
| 2 | 122 ÷ 55 = 2 remainder 12 |
| 3 | 55 ÷ 12 = 4 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 22 | 4070 |
| 182 and 168 | 2184 |
| 96 and 142 | 6816 |
| 122 and 44 | 2684 |
| 41 and 199 | 8159 |