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 |
|---|---|
| 69 and 64 | 4416 |
| 152 and 120 | 2280 |
| 33 and 178 | 5874 |
| 163 and 35 | 5705 |
| 161 and 118 | 18998 |