Least Common Multiple (LCM) of 191 and 103
The least common multiple (LCM) of 191 and 103 is 19673.
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 191 and 103?
First, calculate the GCD of 191 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 103 = 1 remainder 88 |
| 2 | 103 ÷ 88 = 1 remainder 15 |
| 3 | 88 ÷ 15 = 5 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 37 | 1998 |
| 119 and 113 | 13447 |
| 170 and 109 | 18530 |
| 191 and 49 | 9359 |
| 92 and 106 | 4876 |