Least Common Multiple (LCM) of 104 and 123
The least common multiple (LCM) of 104 and 123 is 12792.
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 104 and 123?
First, calculate the GCD of 104 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 123 = 0 remainder 104 |
| 2 | 123 ÷ 104 = 1 remainder 19 |
| 3 | 104 ÷ 19 = 5 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 43 | 3569 |
| 102 and 166 | 8466 |
| 175 and 198 | 34650 |
| 141 and 164 | 23124 |
| 145 and 80 | 2320 |