Least Common Multiple (LCM) of 31 and 194
The least common multiple (LCM) of 31 and 194 is 6014.
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 194?
First, calculate the GCD of 31 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 194 = 0 remainder 31 |
| 2 | 194 ÷ 31 = 6 remainder 8 |
| 3 | 31 ÷ 8 = 3 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 197 | 8471 |
| 115 and 98 | 11270 |
| 47 and 149 | 7003 |
| 56 and 48 | 336 |
| 175 and 163 | 28525 |