Least Common Multiple (LCM) of 106 and 126
The least common multiple (LCM) of 106 and 126 is 6678.
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 106 and 126?
First, calculate the GCD of 106 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 126 = 0 remainder 106 |
| 2 | 126 ÷ 106 = 1 remainder 20 |
| 3 | 106 ÷ 20 = 5 remainder 6 |
| 4 | 20 ÷ 6 = 3 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 143 | 5863 |
| 75 and 20 | 300 |
| 37 and 32 | 1184 |
| 46 and 122 | 2806 |
| 28 and 34 | 476 |