Least Common Multiple (LCM) of 103 and 119
The least common multiple (LCM) of 103 and 119 is 12257.
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 119?
First, calculate the GCD of 103 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 119 = 0 remainder 103 |
| 2 | 119 ÷ 103 = 1 remainder 16 |
| 3 | 103 ÷ 16 = 6 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 |
|---|---|
| 162 and 103 | 16686 |
| 197 and 10 | 1970 |
| 180 and 26 | 2340 |
| 52 and 191 | 9932 |
| 193 and 131 | 25283 |