Least Common Multiple (LCM) of 129 and 177
The least common multiple (LCM) of 129 and 177 is 7611.
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 129 and 177?
First, calculate the GCD of 129 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 177 = 0 remainder 129 |
| 2 | 177 ÷ 129 = 1 remainder 48 |
| 3 | 129 ÷ 48 = 2 remainder 33 |
| 4 | 48 ÷ 33 = 1 remainder 15 |
| 5 | 33 ÷ 15 = 2 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 190 | 1710 |
| 130 and 170 | 2210 |
| 89 and 78 | 6942 |
| 171 and 45 | 855 |
| 144 and 169 | 24336 |