Least Common Multiple (LCM) of 123 and 191
The least common multiple (LCM) of 123 and 191 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 123 and 191?
First, calculate the GCD of 123 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 191 = 0 remainder 123 |
| 2 | 191 ÷ 123 = 1 remainder 68 |
| 3 | 123 ÷ 68 = 1 remainder 55 |
| 4 | 68 ÷ 55 = 1 remainder 13 |
| 5 | 55 ÷ 13 = 4 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 140 | 14980 |
| 97 and 66 | 6402 |
| 51 and 20 | 1020 |
| 56 and 149 | 8344 |
| 187 and 14 | 2618 |