Least Common Multiple (LCM) of 106 and 146
The least common multiple (LCM) of 106 and 146 is 7738.
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 146?
First, calculate the GCD of 106 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 146 = 0 remainder 106 |
| 2 | 146 ÷ 106 = 1 remainder 40 |
| 3 | 106 ÷ 40 = 2 remainder 26 |
| 4 | 40 ÷ 26 = 1 remainder 14 |
| 5 | 26 ÷ 14 = 1 remainder 12 |
| 6 | 14 ÷ 12 = 1 remainder 2 |
| 7 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 188 | 9964 |
| 189 and 90 | 1890 |
| 157 and 101 | 15857 |
| 127 and 81 | 10287 |
| 112 and 44 | 1232 |