Least Common Multiple (LCM) of 199 and 89
The least common multiple (LCM) of 199 and 89 is 17711.
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 199 and 89?
First, calculate the GCD of 199 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 89 = 2 remainder 21 |
| 2 | 89 ÷ 21 = 4 remainder 5 |
| 3 | 21 ÷ 5 = 4 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 35 | 3780 |
| 87 and 51 | 1479 |
| 174 and 123 | 7134 |
| 107 and 94 | 10058 |
| 38 and 35 | 1330 |