Least Common Multiple (LCM) of 123 and 83
The least common multiple (LCM) of 123 and 83 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 123 and 83?
First, calculate the GCD of 123 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 83 = 1 remainder 40 |
| 2 | 83 ÷ 40 = 2 remainder 3 |
| 3 | 40 ÷ 3 = 13 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 150 | 3600 |
| 121 and 191 | 23111 |
| 59 and 75 | 4425 |
| 92 and 13 | 1196 |
| 101 and 105 | 10605 |