Least Common Multiple (LCM) of 174 and 129
The least common multiple (LCM) of 174 and 129 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 174 and 129?
First, calculate the GCD of 174 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 129 = 1 remainder 45 |
| 2 | 129 ÷ 45 = 2 remainder 39 |
| 3 | 45 ÷ 39 = 1 remainder 6 |
| 4 | 39 ÷ 6 = 6 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 33 | 561 |
| 169 and 13 | 169 |
| 119 and 185 | 22015 |
| 44 and 192 | 2112 |
| 142 and 126 | 8946 |