Least Common Multiple (LCM) of 68 and 126
The least common multiple (LCM) of 68 and 126 is 4284.
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 68 and 126?
First, calculate the GCD of 68 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 126 = 0 remainder 68 |
| 2 | 126 ÷ 68 = 1 remainder 58 |
| 3 | 68 ÷ 58 = 1 remainder 10 |
| 4 | 58 ÷ 10 = 5 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 132 | 17556 |
| 10 and 43 | 430 |
| 190 and 185 | 7030 |
| 11 and 26 | 286 |
| 29 and 109 | 3161 |