Least Common Multiple (LCM) of 106 and 46
The least common multiple (LCM) of 106 and 46 is 2438.
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 46?
First, calculate the GCD of 106 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 46 = 2 remainder 14 |
| 2 | 46 ÷ 14 = 3 remainder 4 |
| 3 | 14 ÷ 4 = 3 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 131 | 5633 |
| 169 and 75 | 12675 |
| 110 and 89 | 9790 |
| 122 and 162 | 9882 |
| 177 and 113 | 20001 |