Least Common Multiple (LCM) of 191 and 123
The least common multiple (LCM) of 191 and 123 is 23493.
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 123?
First, calculate the GCD of 191 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 123 = 1 remainder 68 |
| 2 | 123 ÷ 68 = 1 remainder 55 |
| 3 | 68 ÷ 55 = 1 remainder 13 |
| 4 | 55 ÷ 13 = 4 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 60 | 10140 |
| 18 and 116 | 1044 |
| 199 and 101 | 20099 |
| 114 and 23 | 2622 |
| 58 and 13 | 754 |