Least Common Multiple (LCM) of 67 and 159
The least common multiple (LCM) of 67 and 159 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 67 and 159?
First, calculate the GCD of 67 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 159 = 0 remainder 67 |
| 2 | 159 ÷ 67 = 2 remainder 25 |
| 3 | 67 ÷ 25 = 2 remainder 17 |
| 4 | 25 ÷ 17 = 1 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 172 | 4988 |
| 41 and 105 | 4305 |
| 185 and 65 | 2405 |
| 170 and 66 | 5610 |
| 29 and 106 | 3074 |