Least Common Multiple (LCM) of 123 and 193
The least common multiple (LCM) of 123 and 193 is 23739.
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 193?
First, calculate the GCD of 123 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 193 = 0 remainder 123 |
| 2 | 193 ÷ 123 = 1 remainder 70 |
| 3 | 123 ÷ 70 = 1 remainder 53 |
| 4 | 70 ÷ 53 = 1 remainder 17 |
| 5 | 53 ÷ 17 = 3 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 172 | 10836 |
| 187 and 85 | 935 |
| 24 and 36 | 72 |
| 40 and 39 | 1560 |
| 173 and 78 | 13494 |