Least Common Multiple (LCM) of 80 and 126
The least common multiple (LCM) of 80 and 126 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 80 and 126?
First, calculate the GCD of 80 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 126 = 0 remainder 80 |
| 2 | 126 ÷ 80 = 1 remainder 46 |
| 3 | 80 ÷ 46 = 1 remainder 34 |
| 4 | 46 ÷ 34 = 1 remainder 12 |
| 5 | 34 ÷ 12 = 2 remainder 10 |
| 6 | 12 ÷ 10 = 1 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 177 | 9735 |
| 11 and 51 | 561 |
| 11 and 33 | 33 |
| 177 and 31 | 5487 |
| 168 and 120 | 840 |