Least Common Multiple (LCM) of 85 and 135
The least common multiple (LCM) of 85 and 135 is 2295.
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 85 and 135?
First, calculate the GCD of 85 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 135 = 0 remainder 85 |
| 2 | 135 ÷ 85 = 1 remainder 50 |
| 3 | 85 ÷ 50 = 1 remainder 35 |
| 4 | 50 ÷ 35 = 1 remainder 15 |
| 5 | 35 ÷ 15 = 2 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 56 | 1288 |
| 72 and 84 | 504 |
| 143 and 68 | 9724 |
| 30 and 199 | 5970 |
| 198 and 123 | 8118 |