Least Common Multiple (LCM) of 89 and 190
The least common multiple (LCM) of 89 and 190 is 16910.
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 190?
First, calculate the GCD of 89 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 190 = 0 remainder 89 |
| 2 | 190 ÷ 89 = 2 remainder 12 |
| 3 | 89 ÷ 12 = 7 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 168 | 33432 |
| 42 and 195 | 2730 |
| 180 and 30 | 180 |
| 37 and 72 | 2664 |
| 146 and 18 | 1314 |