Least Common Multiple (LCM) of 83 and 22
The least common multiple (LCM) of 83 and 22 is 1826.
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 83 and 22?
First, calculate the GCD of 83 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 22 = 3 remainder 17 |
| 2 | 22 ÷ 17 = 1 remainder 5 |
| 3 | 17 ÷ 5 = 3 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 74 | 4884 |
| 33 and 24 | 264 |
| 91 and 191 | 17381 |
| 116 and 115 | 13340 |
| 198 and 75 | 4950 |