Least Common Multiple (LCM) of 117 and 177
The least common multiple (LCM) of 117 and 177 is 6903.
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 117 and 177?
First, calculate the GCD of 117 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 177 = 0 remainder 117 |
| 2 | 177 ÷ 117 = 1 remainder 60 |
| 3 | 117 ÷ 60 = 1 remainder 57 |
| 4 | 60 ÷ 57 = 1 remainder 3 |
| 5 | 57 ÷ 3 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 63 | 1449 |
| 65 and 49 | 3185 |
| 140 and 57 | 7980 |
| 63 and 27 | 189 |
| 29 and 82 | 2378 |