Least Common Multiple (LCM) of 123 and 183
The least common multiple (LCM) of 123 and 183 is 7503.
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 183?
First, calculate the GCD of 123 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 183 = 0 remainder 123 |
| 2 | 183 ÷ 123 = 1 remainder 60 |
| 3 | 123 ÷ 60 = 2 remainder 3 |
| 4 | 60 ÷ 3 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 138 | 5520 |
| 106 and 13 | 1378 |
| 44 and 97 | 4268 |
| 48 and 90 | 720 |
| 51 and 67 | 3417 |