Least Common Multiple (LCM) of 109 and 190
The least common multiple (LCM) of 109 and 190 is 20710.
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 109 and 190?
First, calculate the GCD of 109 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 190 = 0 remainder 109 |
| 2 | 190 ÷ 109 = 1 remainder 81 |
| 3 | 109 ÷ 81 = 1 remainder 28 |
| 4 | 81 ÷ 28 = 2 remainder 25 |
| 5 | 28 ÷ 25 = 1 remainder 3 |
| 6 | 25 ÷ 3 = 8 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 85 | 9945 |
| 47 and 31 | 1457 |
| 151 and 95 | 14345 |
| 85 and 141 | 11985 |
| 38 and 16 | 304 |