Least Common Multiple (LCM) of 116 and 190
The least common multiple (LCM) of 116 and 190 is 11020.
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 116 and 190?
First, calculate the GCD of 116 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 190 = 0 remainder 116 |
| 2 | 190 ÷ 116 = 1 remainder 74 |
| 3 | 116 ÷ 74 = 1 remainder 42 |
| 4 | 74 ÷ 42 = 1 remainder 32 |
| 5 | 42 ÷ 32 = 1 remainder 10 |
| 6 | 32 ÷ 10 = 3 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 11 | 2068 |
| 96 and 97 | 9312 |
| 193 and 175 | 33775 |
| 10 and 20 | 20 |
| 109 and 178 | 19402 |