Least Common Multiple (LCM) of 123 and 104
The least common multiple (LCM) of 123 and 104 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 123 and 104?
First, calculate the GCD of 123 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 104 = 1 remainder 19 |
| 2 | 104 ÷ 19 = 5 remainder 9 |
| 3 | 19 ÷ 9 = 2 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 106 | 1802 |
| 43 and 42 | 1806 |
| 171 and 167 | 28557 |
| 87 and 75 | 2175 |
| 80 and 66 | 2640 |