Least Common Multiple (LCM) of 89 and 142
The least common multiple (LCM) of 89 and 142 is 12638.
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 89 and 142?
First, calculate the GCD of 89 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 142 = 0 remainder 89 |
| 2 | 142 ÷ 89 = 1 remainder 53 |
| 3 | 89 ÷ 53 = 1 remainder 36 |
| 4 | 53 ÷ 36 = 1 remainder 17 |
| 5 | 36 ÷ 17 = 2 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 172 | 22876 |
| 109 and 17 | 1853 |
| 129 and 81 | 3483 |
| 67 and 199 | 13333 |
| 43 and 72 | 3096 |