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 |
|---|---|
| 132 and 174 | 3828 |
| 193 and 69 | 13317 |
| 167 and 133 | 22211 |
| 88 and 38 | 1672 |
| 53 and 179 | 9487 |