Least Common Multiple (LCM) of 176 and 129
The least common multiple (LCM) of 176 and 129 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 176 and 129?
First, calculate the GCD of 176 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 129 = 1 remainder 47 |
| 2 | 129 ÷ 47 = 2 remainder 35 |
| 3 | 47 ÷ 35 = 1 remainder 12 |
| 4 | 35 ÷ 12 = 2 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 175 | 350 |
| 102 and 106 | 5406 |
| 11 and 11 | 11 |
| 15 and 145 | 435 |
| 141 and 37 | 5217 |