Least Common Multiple (LCM) of 135 and 30
The least common multiple (LCM) of 135 and 30 is 270.
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 30?
First, calculate the GCD of 135 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 30 = 4 remainder 15 |
| 2 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 133 | 1197 |
| 143 and 60 | 8580 |
| 86 and 109 | 9374 |
| 120 and 29 | 3480 |
| 89 and 110 | 9790 |