Least Common Multiple (LCM) of 135 and 123
The least common multiple (LCM) of 135 and 123 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 135 and 123?
First, calculate the GCD of 135 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 123 = 1 remainder 12 |
| 2 | 123 ÷ 12 = 10 remainder 3 |
| 3 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 120 | 4440 |
| 151 and 47 | 7097 |
| 140 and 40 | 280 |
| 48 and 45 | 720 |
| 30 and 45 | 90 |