Least Common Multiple (LCM) of 193 and 31
The least common multiple (LCM) of 193 and 31 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 193 and 31?
First, calculate the GCD of 193 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 31 = 6 remainder 7 |
| 2 | 31 ÷ 7 = 4 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 77 | 9856 |
| 104 and 135 | 14040 |
| 193 and 158 | 30494 |
| 58 and 115 | 6670 |
| 185 and 115 | 4255 |