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 |
|---|---|
| 109 and 91 | 9919 |
| 162 and 160 | 12960 |
| 129 and 98 | 12642 |
| 131 and 142 | 18602 |
| 45 and 99 | 495 |