Least Common Multiple (LCM) of 31 and 129
The least common multiple (LCM) of 31 and 129 is 3999.
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 31 and 129?
First, calculate the GCD of 31 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 129 = 0 remainder 31 |
| 2 | 129 ÷ 31 = 4 remainder 5 |
| 3 | 31 ÷ 5 = 6 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 137 | 6165 |
| 170 and 166 | 14110 |
| 55 and 138 | 7590 |
| 76 and 199 | 15124 |
| 171 and 197 | 33687 |