Least Common Multiple (LCM) of 193 and 123
The least common multiple (LCM) of 193 and 123 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 193 and 123?
First, calculate the GCD of 193 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 123 = 1 remainder 70 |
| 2 | 123 ÷ 70 = 1 remainder 53 |
| 3 | 70 ÷ 53 = 1 remainder 17 |
| 4 | 53 ÷ 17 = 3 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 177 | 2478 |
| 112 and 27 | 3024 |
| 26 and 116 | 1508 |
| 123 and 46 | 5658 |
| 140 and 71 | 9940 |