Least Common Multiple (LCM) of 19 and 135
The least common multiple (LCM) of 19 and 135 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 19 and 135?
First, calculate the GCD of 19 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 135 = 0 remainder 19 |
| 2 | 135 ÷ 19 = 7 remainder 2 |
| 3 | 19 ÷ 2 = 9 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 116 | 12412 |
| 23 and 54 | 1242 |
| 154 and 68 | 5236 |
| 187 and 37 | 6919 |
| 128 and 195 | 24960 |