Least Common Multiple (LCM) of 123 and 114
The least common multiple (LCM) of 123 and 114 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 123 and 114?
First, calculate the GCD of 123 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 114 = 1 remainder 9 |
| 2 | 114 ÷ 9 = 12 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 83 | 16517 |
| 185 and 75 | 2775 |
| 90 and 72 | 360 |
| 115 and 165 | 3795 |
| 196 and 136 | 6664 |