Least Common Multiple (LCM) of 103 and 190
The least common multiple (LCM) of 103 and 190 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 103 and 190?
First, calculate the GCD of 103 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 190 = 0 remainder 103 |
| 2 | 190 ÷ 103 = 1 remainder 87 |
| 3 | 103 ÷ 87 = 1 remainder 16 |
| 4 | 87 ÷ 16 = 5 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 30 | 810 |
| 59 and 176 | 10384 |
| 169 and 168 | 28392 |
| 48 and 128 | 384 |
| 163 and 31 | 5053 |