Least Common Multiple (LCM) of 114 and 123
The least common multiple (LCM) of 114 and 123 is 4674.
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 114 and 123?
First, calculate the GCD of 114 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 123 = 0 remainder 114 |
| 2 | 123 ÷ 114 = 1 remainder 9 |
| 3 | 114 ÷ 9 = 12 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 180 | 2340 |
| 107 and 135 | 14445 |
| 186 and 146 | 13578 |
| 31 and 106 | 3286 |
| 188 and 115 | 21620 |