Least Common Multiple (LCM) of 126 and 180
The least common multiple (LCM) of 126 and 180 is 1260.
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 180?
First, calculate the GCD of 126 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 180 = 0 remainder 126 |
| 2 | 180 ÷ 126 = 1 remainder 54 |
| 3 | 126 ÷ 54 = 2 remainder 18 |
| 4 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 134 | 21842 |
| 60 and 97 | 5820 |
| 180 and 165 | 1980 |
| 85 and 71 | 6035 |
| 127 and 65 | 8255 |