Least Common Multiple (LCM) of 74 and 129
The least common multiple (LCM) of 74 and 129 is 9546.
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 74 and 129?
First, calculate the GCD of 74 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 129 = 0 remainder 74 |
| 2 | 129 ÷ 74 = 1 remainder 55 |
| 3 | 74 ÷ 55 = 1 remainder 19 |
| 4 | 55 ÷ 19 = 2 remainder 17 |
| 5 | 19 ÷ 17 = 1 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 186 | 5394 |
| 86 and 182 | 7826 |
| 56 and 46 | 1288 |
| 37 and 158 | 5846 |
| 168 and 46 | 3864 |