Least Common Multiple (LCM) of 123 and 108
The least common multiple (LCM) of 123 and 108 is 4428.
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 108?
First, calculate the GCD of 123 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 108 = 1 remainder 15 |
| 2 | 108 ÷ 15 = 7 remainder 3 |
| 3 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 59 | 5605 |
| 169 and 86 | 14534 |
| 74 and 199 | 14726 |
| 140 and 45 | 1260 |
| 135 and 51 | 2295 |