Least Common Multiple (LCM) of 85 and 159
The least common multiple (LCM) of 85 and 159 is 13515.
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 159?
First, calculate the GCD of 85 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 159 = 0 remainder 85 |
| 2 | 159 ÷ 85 = 1 remainder 74 |
| 3 | 85 ÷ 74 = 1 remainder 11 |
| 4 | 74 ÷ 11 = 6 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 34 | 2652 |
| 73 and 186 | 13578 |
| 60 and 146 | 4380 |
| 84 and 10 | 420 |
| 31 and 65 | 2015 |