Least Common Multiple (LCM) of 85 and 131
The least common multiple (LCM) of 85 and 131 is 11135.
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 131?
First, calculate the GCD of 85 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 131 = 0 remainder 85 |
| 2 | 131 ÷ 85 = 1 remainder 46 |
| 3 | 85 ÷ 46 = 1 remainder 39 |
| 4 | 46 ÷ 39 = 1 remainder 7 |
| 5 | 39 ÷ 7 = 5 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 108 | 1188 |
| 190 and 83 | 15770 |
| 187 and 191 | 35717 |
| 54 and 100 | 2700 |
| 144 and 158 | 11376 |