Least Common Multiple (LCM) of 135 and 155
The least common multiple (LCM) of 135 and 155 is 4185.
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 155?
First, calculate the GCD of 135 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 155 = 0 remainder 135 |
| 2 | 155 ÷ 135 = 1 remainder 20 |
| 3 | 135 ÷ 20 = 6 remainder 15 |
| 4 | 20 ÷ 15 = 1 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 47 | 6345 |
| 128 and 109 | 13952 |
| 24 and 46 | 552 |
| 54 and 169 | 9126 |
| 20 and 60 | 60 |