Least Common Multiple (LCM) of 71 and 197
The least common multiple (LCM) of 71 and 197 is 13987.
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 71 and 197?
First, calculate the GCD of 71 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 197 = 0 remainder 71 |
| 2 | 197 ÷ 71 = 2 remainder 55 |
| 3 | 71 ÷ 55 = 1 remainder 16 |
| 4 | 55 ÷ 16 = 3 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 145 | 870 |
| 159 and 137 | 21783 |
| 30 and 188 | 2820 |
| 181 and 42 | 7602 |
| 99 and 99 | 99 |