Least Common Multiple (LCM) of 31 and 196
The least common multiple (LCM) of 31 and 196 is 6076.
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 196?
First, calculate the GCD of 31 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 196 = 0 remainder 31 |
| 2 | 196 ÷ 31 = 6 remainder 10 |
| 3 | 31 ÷ 10 = 3 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 197 | 27580 |
| 103 and 174 | 17922 |
| 120 and 147 | 5880 |
| 176 and 122 | 10736 |
| 98 and 145 | 14210 |