Least Common Multiple (LCM) of 126 and 135
The least common multiple (LCM) of 126 and 135 is 1890.
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 135?
First, calculate the GCD of 126 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 135 = 0 remainder 126 |
| 2 | 135 ÷ 126 = 1 remainder 9 |
| 3 | 126 ÷ 9 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 12 | 72 |
| 24 and 12 | 24 |
| 124 and 10 | 620 |
| 59 and 171 | 10089 |
| 177 and 70 | 12390 |