Least Common Multiple (LCM) of 103 and 19
The least common multiple (LCM) of 103 and 19 is 1957.
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 19?
First, calculate the GCD of 103 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 19 = 5 remainder 8 |
| 2 | 19 ÷ 8 = 2 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 117 | 4095 |
| 94 and 50 | 2350 |
| 40 and 137 | 5480 |
| 180 and 19 | 3420 |
| 175 and 73 | 12775 |