Least Common Multiple (LCM) of 126 and 81
The least common multiple (LCM) of 126 and 81 is 1134.
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 81?
First, calculate the GCD of 126 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 81 = 1 remainder 45 |
| 2 | 81 ÷ 45 = 1 remainder 36 |
| 3 | 45 ÷ 36 = 1 remainder 9 |
| 4 | 36 ÷ 9 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 57 | 7125 |
| 139 and 141 | 19599 |
| 179 and 63 | 11277 |
| 102 and 187 | 1122 |
| 135 and 139 | 18765 |