Least Common Multiple (LCM) of 123 and 135
The least common multiple (LCM) of 123 and 135 is 5535.
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 135?
First, calculate the GCD of 123 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 135 = 0 remainder 123 |
| 2 | 135 ÷ 123 = 1 remainder 12 |
| 3 | 123 ÷ 12 = 10 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 111 | 4440 |
| 194 and 154 | 14938 |
| 75 and 78 | 1950 |
| 150 and 188 | 14100 |
| 80 and 126 | 5040 |