Least Common Multiple (LCM) of 126 and 192
The least common multiple (LCM) of 126 and 192 is 4032.
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 192?
First, calculate the GCD of 126 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 192 = 0 remainder 126 |
| 2 | 192 ÷ 126 = 1 remainder 66 |
| 3 | 126 ÷ 66 = 1 remainder 60 |
| 4 | 66 ÷ 60 = 1 remainder 6 |
| 5 | 60 ÷ 6 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 145 | 12760 |
| 186 and 16 | 1488 |
| 34 and 163 | 5542 |
| 82 and 119 | 9758 |
| 15 and 43 | 645 |