Least Common Multiple (LCM) of 177 and 114
The least common multiple (LCM) of 177 and 114 is 6726.
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 114?
First, calculate the GCD of 177 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 114 = 1 remainder 63 |
| 2 | 114 ÷ 63 = 1 remainder 51 |
| 3 | 63 ÷ 51 = 1 remainder 12 |
| 4 | 51 ÷ 12 = 4 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 126 | 630 |
| 66 and 66 | 66 |
| 10 and 37 | 370 |
| 106 and 49 | 5194 |
| 49 and 51 | 2499 |