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 |
|---|---|
| 37 and 30 | 1110 |
| 97 and 144 | 13968 |
| 168 and 99 | 5544 |
| 149 and 155 | 23095 |
| 85 and 171 | 14535 |