Least Common Multiple (LCM) of 123 and 115
The least common multiple (LCM) of 123 and 115 is 14145.
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 115?
First, calculate the GCD of 123 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 115 = 1 remainder 8 |
| 2 | 115 ÷ 8 = 14 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 26 | 390 |
| 40 and 21 | 840 |
| 23 and 190 | 4370 |
| 199 and 41 | 8159 |
| 49 and 16 | 784 |