Least Common Multiple (LCM) of 85 and 136
The least common multiple (LCM) of 85 and 136 is 680.
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 136?
First, calculate the GCD of 85 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 136 = 0 remainder 85 |
| 2 | 136 ÷ 85 = 1 remainder 51 |
| 3 | 85 ÷ 51 = 1 remainder 34 |
| 4 | 51 ÷ 34 = 1 remainder 17 |
| 5 | 34 ÷ 17 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 108 | 756 |
| 133 and 135 | 17955 |
| 147 and 158 | 23226 |
| 24 and 60 | 120 |
| 112 and 130 | 7280 |