Least Common Multiple (LCM) of 22 and 83
The least common multiple (LCM) of 22 and 83 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 22 and 83?
First, calculate the GCD of 22 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 83 = 0 remainder 22 |
| 2 | 83 ÷ 22 = 3 remainder 17 |
| 3 | 22 ÷ 17 = 1 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 172 | 18060 |
| 80 and 160 | 160 |
| 130 and 180 | 2340 |
| 12 and 190 | 1140 |
| 148 and 140 | 5180 |