Least Common Multiple (LCM) of 59 and 83
The least common multiple (LCM) of 59 and 83 is 4897.
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 83?
First, calculate the GCD of 59 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 83 = 0 remainder 59 |
| 2 | 83 ÷ 59 = 1 remainder 24 |
| 3 | 59 ÷ 24 = 2 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 88 | 5720 |
| 192 and 15 | 960 |
| 104 and 61 | 6344 |
| 93 and 105 | 3255 |
| 55 and 91 | 5005 |