Least Common Multiple (LCM) of 89 and 82
The least common multiple (LCM) of 89 and 82 is 7298.
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 89 and 82?
First, calculate the GCD of 89 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 82 = 1 remainder 7 |
| 2 | 82 ÷ 7 = 11 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 172 | 3612 |
| 25 and 104 | 2600 |
| 120 and 127 | 15240 |
| 166 and 116 | 9628 |
| 40 and 119 | 4760 |