Least Common Multiple (LCM) of 126 and 163
The least common multiple (LCM) of 126 and 163 is 20538.
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 163?
First, calculate the GCD of 126 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 163 = 0 remainder 126 |
| 2 | 163 ÷ 126 = 1 remainder 37 |
| 3 | 126 ÷ 37 = 3 remainder 15 |
| 4 | 37 ÷ 15 = 2 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 90 | 90 |
| 53 and 90 | 4770 |
| 25 and 193 | 4825 |
| 165 and 26 | 4290 |
| 17 and 37 | 629 |