Least Common Multiple (LCM) of 83 and 123
The least common multiple (LCM) of 83 and 123 is 10209.
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 123?
First, calculate the GCD of 83 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 123 = 0 remainder 83 |
| 2 | 123 ÷ 83 = 1 remainder 40 |
| 3 | 83 ÷ 40 = 2 remainder 3 |
| 4 | 40 ÷ 3 = 13 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 29 | 4379 |
| 28 and 197 | 5516 |
| 39 and 136 | 5304 |
| 184 and 164 | 7544 |
| 135 and 14 | 1890 |