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 |
|---|---|
| 141 and 100 | 14100 |
| 84 and 63 | 252 |
| 50 and 15 | 150 |
| 171 and 142 | 24282 |
| 159 and 63 | 3339 |