Least Common Multiple (LCM) of 71 and 49
The least common multiple (LCM) of 71 and 49 is 3479.
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 49?
First, calculate the GCD of 71 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 49 = 1 remainder 22 |
| 2 | 49 ÷ 22 = 2 remainder 5 |
| 3 | 22 ÷ 5 = 4 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 96 | 10272 |
| 70 and 188 | 6580 |
| 171 and 137 | 23427 |
| 26 and 111 | 2886 |
| 187 and 94 | 17578 |