Least Common Multiple (LCM) of 190 and 103
The least common multiple (LCM) of 190 and 103 is 19570.
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 190 and 103?
First, calculate the GCD of 190 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 103 = 1 remainder 87 |
| 2 | 103 ÷ 87 = 1 remainder 16 |
| 3 | 87 ÷ 16 = 5 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 182 | 1820 |
| 180 and 115 | 4140 |
| 115 and 183 | 21045 |
| 39 and 196 | 7644 |
| 69 and 103 | 7107 |