Least Common Multiple (LCM) of 126 and 80
The least common multiple (LCM) of 126 and 80 is 5040.
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 80?
First, calculate the GCD of 126 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 80 = 1 remainder 46 |
| 2 | 80 ÷ 46 = 1 remainder 34 |
| 3 | 46 ÷ 34 = 1 remainder 12 |
| 4 | 34 ÷ 12 = 2 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 143 | 16302 |
| 127 and 180 | 22860 |
| 133 and 137 | 18221 |
| 33 and 46 | 1518 |
| 185 and 54 | 9990 |