Least Common Multiple (LCM) of 55 and 83
The least common multiple (LCM) of 55 and 83 is 4565.
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 55 and 83?
First, calculate the GCD of 55 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 83 = 0 remainder 55 |
| 2 | 83 ÷ 55 = 1 remainder 28 |
| 3 | 55 ÷ 28 = 1 remainder 27 |
| 4 | 28 ÷ 27 = 1 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 102 | 918 |
| 188 and 102 | 9588 |
| 20 and 100 | 100 |
| 173 and 193 | 33389 |
| 104 and 42 | 2184 |