Least Common Multiple (LCM) of 126 and 31
The least common multiple (LCM) of 126 and 31 is 3906.
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 126 and 31?
First, calculate the GCD of 126 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 31 = 4 remainder 2 |
| 2 | 31 ÷ 2 = 15 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 10 | 10 |
| 52 and 65 | 260 |
| 173 and 76 | 13148 |
| 140 and 148 | 5180 |
| 31 and 14 | 434 |