Least Common Multiple (LCM) of 71 and 114
The least common multiple (LCM) of 71 and 114 is 8094.
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 114?
First, calculate the GCD of 71 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 114 = 0 remainder 71 |
| 2 | 114 ÷ 71 = 1 remainder 43 |
| 3 | 71 ÷ 43 = 1 remainder 28 |
| 4 | 43 ÷ 28 = 1 remainder 15 |
| 5 | 28 ÷ 15 = 1 remainder 13 |
| 6 | 15 ÷ 13 = 1 remainder 2 |
| 7 | 13 ÷ 2 = 6 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 35 | 2135 |
| 14 and 125 | 1750 |
| 156 and 177 | 9204 |
| 28 and 31 | 868 |
| 135 and 78 | 3510 |