Least Common Multiple (LCM) of 135 and 19
The least common multiple (LCM) of 135 and 19 is 2565.
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 19?
First, calculate the GCD of 135 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 19 = 7 remainder 2 |
| 2 | 19 ÷ 2 = 9 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 50 | 150 |
| 60 and 145 | 1740 |
| 150 and 10 | 150 |
| 104 and 173 | 17992 |
| 184 and 111 | 20424 |