Least Common Multiple (LCM) of 83 and 177
The least common multiple (LCM) of 83 and 177 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 83 and 177?
First, calculate the GCD of 83 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 177 = 0 remainder 83 |
| 2 | 177 ÷ 83 = 2 remainder 11 |
| 3 | 83 ÷ 11 = 7 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 134 | 7638 |
| 39 and 129 | 1677 |
| 39 and 196 | 7644 |
| 88 and 130 | 5720 |
| 21 and 141 | 987 |