Least Common Multiple (LCM) of 71 and 89
The least common multiple (LCM) of 71 and 89 is 6319.
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 89?
First, calculate the GCD of 71 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 89 = 0 remainder 71 |
| 2 | 89 ÷ 71 = 1 remainder 18 |
| 3 | 71 ÷ 18 = 3 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 68 | 1564 |
| 20 and 114 | 1140 |
| 187 and 22 | 374 |
| 130 and 66 | 4290 |
| 59 and 120 | 7080 |