Least Common Multiple (LCM) of 135 and 85
The least common multiple (LCM) of 135 and 85 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 135 and 85?
First, calculate the GCD of 135 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 85 = 1 remainder 50 |
| 2 | 85 ÷ 50 = 1 remainder 35 |
| 3 | 50 ÷ 35 = 1 remainder 15 |
| 4 | 35 ÷ 15 = 2 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 40 | 200 |
| 37 and 16 | 592 |
| 15 and 106 | 1590 |
| 32 and 155 | 4960 |
| 49 and 97 | 4753 |