Least Common Multiple (LCM) of 71 and 131
The least common multiple (LCM) of 71 and 131 is 9301.
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 131?
First, calculate the GCD of 71 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 131 = 0 remainder 71 |
| 2 | 131 ÷ 71 = 1 remainder 60 |
| 3 | 71 ÷ 60 = 1 remainder 11 |
| 4 | 60 ÷ 11 = 5 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 147 | 16611 |
| 60 and 10 | 60 |
| 142 and 184 | 13064 |
| 135 and 177 | 7965 |
| 106 and 54 | 2862 |