Least Common Multiple (LCM) of 86 and 159
The least common multiple (LCM) of 86 and 159 is 13674.
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 86 and 159?
First, calculate the GCD of 86 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 159 = 0 remainder 86 |
| 2 | 159 ÷ 86 = 1 remainder 73 |
| 3 | 86 ÷ 73 = 1 remainder 13 |
| 4 | 73 ÷ 13 = 5 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 70 | 2310 |
| 22 and 83 | 1826 |
| 174 and 107 | 18618 |
| 45 and 192 | 2880 |
| 50 and 120 | 600 |