Least Common Multiple (LCM) of 135 and 195
The least common multiple (LCM) of 135 and 195 is 1755.
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 195?
First, calculate the GCD of 135 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 195 = 0 remainder 135 |
| 2 | 195 ÷ 135 = 1 remainder 60 |
| 3 | 135 ÷ 60 = 2 remainder 15 |
| 4 | 60 ÷ 15 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 52 | 1716 |
| 32 and 90 | 1440 |
| 146 and 128 | 9344 |
| 55 and 86 | 4730 |
| 143 and 106 | 15158 |