Least Common Multiple (LCM) of 159 and 67
The least common multiple (LCM) of 159 and 67 is 10653.
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 67?
First, calculate the GCD of 159 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 67 = 2 remainder 25 |
| 2 | 67 ÷ 25 = 2 remainder 17 |
| 3 | 25 ÷ 17 = 1 remainder 8 |
| 4 | 17 ÷ 8 = 2 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 191 | 27886 |
| 199 and 178 | 35422 |
| 189 and 190 | 35910 |
| 162 and 162 | 162 |
| 122 and 104 | 6344 |