Least Common Multiple (LCM) of 126 and 177
The least common multiple (LCM) of 126 and 177 is 7434.
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 126 and 177?
First, calculate the GCD of 126 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 177 = 0 remainder 126 |
| 2 | 177 ÷ 126 = 1 remainder 51 |
| 3 | 126 ÷ 51 = 2 remainder 24 |
| 4 | 51 ÷ 24 = 2 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 122 | 5246 |
| 125 and 76 | 9500 |
| 85 and 76 | 6460 |
| 128 and 107 | 13696 |
| 163 and 69 | 11247 |