Least Common Multiple (LCM) of 59 and 86
The least common multiple (LCM) of 59 and 86 is 5074.
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 59 and 86?
First, calculate the GCD of 59 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 86 = 0 remainder 59 |
| 2 | 86 ÷ 59 = 1 remainder 27 |
| 3 | 59 ÷ 27 = 2 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 105 | 8715 |
| 164 and 55 | 9020 |
| 105 and 44 | 4620 |
| 149 and 14 | 2086 |
| 14 and 110 | 770 |