Least Common Multiple (LCM) of 110 and 135
The least common multiple (LCM) of 110 and 135 is 2970.
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 110 and 135?
First, calculate the GCD of 110 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 135 = 0 remainder 110 |
| 2 | 135 ÷ 110 = 1 remainder 25 |
| 3 | 110 ÷ 25 = 4 remainder 10 |
| 4 | 25 ÷ 10 = 2 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 35 | 3605 |
| 195 and 181 | 35295 |
| 14 and 196 | 196 |
| 168 and 95 | 15960 |
| 29 and 18 | 522 |