Least Common Multiple (LCM) of 115 and 123
The least common multiple (LCM) of 115 and 123 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 115 and 123?
First, calculate the GCD of 115 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 123 = 0 remainder 115 |
| 2 | 123 ÷ 115 = 1 remainder 8 |
| 3 | 115 ÷ 8 = 14 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 138 | 2208 |
| 89 and 125 | 11125 |
| 135 and 153 | 2295 |
| 52 and 144 | 1872 |
| 38 and 152 | 152 |