Least Common Multiple (LCM) of 108 and 126
The least common multiple (LCM) of 108 and 126 is 756.
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 108 and 126?
First, calculate the GCD of 108 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 126 = 0 remainder 108 |
| 2 | 126 ÷ 108 = 1 remainder 18 |
| 3 | 108 ÷ 18 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 67 | 7102 |
| 190 and 176 | 16720 |
| 104 and 138 | 7176 |
| 138 and 49 | 6762 |
| 109 and 143 | 15587 |