Least Common Multiple (LCM) of 129 and 178
The least common multiple (LCM) of 129 and 178 is 22962.
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 178?
First, calculate the GCD of 129 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 178 = 0 remainder 129 |
| 2 | 178 ÷ 129 = 1 remainder 49 |
| 3 | 129 ÷ 49 = 2 remainder 31 |
| 4 | 49 ÷ 31 = 1 remainder 18 |
| 5 | 31 ÷ 18 = 1 remainder 13 |
| 6 | 18 ÷ 13 = 1 remainder 5 |
| 7 | 13 ÷ 5 = 2 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 108 | 1080 |
| 112 and 144 | 1008 |
| 22 and 199 | 4378 |
| 120 and 107 | 12840 |
| 31 and 168 | 5208 |