Least Common Multiple (LCM) of 129 and 174
The least common multiple (LCM) of 129 and 174 is 7482.
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 174?
First, calculate the GCD of 129 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 174 = 0 remainder 129 |
| 2 | 174 ÷ 129 = 1 remainder 45 |
| 3 | 129 ÷ 45 = 2 remainder 39 |
| 4 | 45 ÷ 39 = 1 remainder 6 |
| 5 | 39 ÷ 6 = 6 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 48 | 336 |
| 67 and 38 | 2546 |
| 70 and 166 | 5810 |
| 184 and 64 | 1472 |
| 194 and 112 | 10864 |