Least Common Multiple (LCM) of 27 and 83
The least common multiple (LCM) of 27 and 83 is 2241.
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 27 and 83?
First, calculate the GCD of 27 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 83 = 0 remainder 27 |
| 2 | 83 ÷ 27 = 3 remainder 2 |
| 3 | 27 ÷ 2 = 13 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 113 | 3164 |
| 78 and 55 | 4290 |
| 134 and 200 | 13400 |
| 40 and 112 | 560 |
| 30 and 183 | 1830 |