Least Common Multiple (LCM) of 31 and 193
The least common multiple (LCM) of 31 and 193 is 5983.
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 193?
First, calculate the GCD of 31 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 193 = 0 remainder 31 |
| 2 | 193 ÷ 31 = 6 remainder 7 |
| 3 | 31 ÷ 7 = 4 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 132 | 132 |
| 189 and 180 | 3780 |
| 62 and 105 | 6510 |
| 135 and 193 | 26055 |
| 80 and 187 | 14960 |