Least Common Multiple (LCM) of 159 and 86
The least common multiple (LCM) of 159 and 86 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 159 and 86?
First, calculate the GCD of 159 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 86 = 1 remainder 73 |
| 2 | 86 ÷ 73 = 1 remainder 13 |
| 3 | 73 ÷ 13 = 5 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 89 | 3115 |
| 186 and 176 | 16368 |
| 109 and 49 | 5341 |
| 90 and 19 | 1710 |
| 119 and 63 | 1071 |