Least Common Multiple (LCM) of 106 and 188
The least common multiple (LCM) of 106 and 188 is 9964.
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 188?
First, calculate the GCD of 106 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 188 = 0 remainder 106 |
| 2 | 188 ÷ 106 = 1 remainder 82 |
| 3 | 106 ÷ 82 = 1 remainder 24 |
| 4 | 82 ÷ 24 = 3 remainder 10 |
| 5 | 24 ÷ 10 = 2 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 84 | 6636 |
| 186 and 109 | 20274 |
| 114 and 46 | 2622 |
| 128 and 132 | 4224 |
| 151 and 75 | 11325 |