Least Common Multiple (LCM) of 126 and 193
The least common multiple (LCM) of 126 and 193 is 24318.
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 126 and 193?
First, calculate the GCD of 126 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 193 = 0 remainder 126 |
| 2 | 193 ÷ 126 = 1 remainder 67 |
| 3 | 126 ÷ 67 = 1 remainder 59 |
| 4 | 67 ÷ 59 = 1 remainder 8 |
| 5 | 59 ÷ 8 = 7 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 145 | 8265 |
| 191 and 159 | 30369 |
| 11 and 102 | 1122 |
| 87 and 114 | 3306 |
| 177 and 61 | 10797 |