Least Common Multiple (LCM) of 177 and 83
The least common multiple (LCM) of 177 and 83 is 14691.
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 83?
First, calculate the GCD of 177 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 83 = 2 remainder 11 |
| 2 | 83 ÷ 11 = 7 remainder 6 |
| 3 | 11 ÷ 6 = 1 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 30 | 1290 |
| 176 and 74 | 6512 |
| 116 and 182 | 10556 |
| 71 and 43 | 3053 |
| 194 and 62 | 6014 |