Least Common Multiple (LCM) of 71 and 97
The least common multiple (LCM) of 71 and 97 is 6887.
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 97?
First, calculate the GCD of 71 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 97 = 0 remainder 71 |
| 2 | 97 ÷ 71 = 1 remainder 26 |
| 3 | 71 ÷ 26 = 2 remainder 19 |
| 4 | 26 ÷ 19 = 1 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 134 | 134 |
| 130 and 153 | 19890 |
| 196 and 157 | 30772 |
| 91 and 161 | 2093 |
| 150 and 188 | 14100 |