Least Common Multiple (LCM) of 108 and 123
The least common multiple (LCM) of 108 and 123 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 108 and 123?
First, calculate the GCD of 108 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 123 = 0 remainder 108 |
| 2 | 123 ÷ 108 = 1 remainder 15 |
| 3 | 108 ÷ 15 = 7 remainder 3 |
| 4 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 177 | 18939 |
| 138 and 172 | 11868 |
| 41 and 43 | 1763 |
| 194 and 144 | 13968 |
| 40 and 56 | 280 |