Least Common Multiple (LCM) of 31 and 118
The least common multiple (LCM) of 31 and 118 is 3658.
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 118?
First, calculate the GCD of 31 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 118 = 0 remainder 31 |
| 2 | 118 ÷ 31 = 3 remainder 25 |
| 3 | 31 ÷ 25 = 1 remainder 6 |
| 4 | 25 ÷ 6 = 4 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 189 | 756 |
| 66 and 171 | 3762 |
| 25 and 31 | 775 |
| 45 and 11 | 495 |
| 71 and 40 | 2840 |