Least Common Multiple (LCM) of 83 and 145
The least common multiple (LCM) of 83 and 145 is 12035.
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 145?
First, calculate the GCD of 83 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 145 = 0 remainder 83 |
| 2 | 145 ÷ 83 = 1 remainder 62 |
| 3 | 83 ÷ 62 = 1 remainder 21 |
| 4 | 62 ÷ 21 = 2 remainder 20 |
| 5 | 21 ÷ 20 = 1 remainder 1 |
| 6 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 188 | 5076 |
| 189 and 196 | 5292 |
| 26 and 77 | 2002 |
| 102 and 166 | 8466 |
| 30 and 22 | 330 |