Least Common Multiple (LCM) of 129 and 176
The least common multiple (LCM) of 129 and 176 is 22704.
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 176?
First, calculate the GCD of 129 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 176 = 0 remainder 129 |
| 2 | 176 ÷ 129 = 1 remainder 47 |
| 3 | 129 ÷ 47 = 2 remainder 35 |
| 4 | 47 ÷ 35 = 1 remainder 12 |
| 5 | 35 ÷ 12 = 2 remainder 11 |
| 6 | 12 ÷ 11 = 1 remainder 1 |
| 7 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 74 | 1554 |
| 120 and 21 | 840 |
| 150 and 49 | 7350 |
| 135 and 66 | 2970 |
| 177 and 172 | 30444 |