Least Common Multiple (LCM) of 188 and 106
The least common multiple (LCM) of 188 and 106 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 188 and 106?
First, calculate the GCD of 188 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 106 = 1 remainder 82 |
| 2 | 106 ÷ 82 = 1 remainder 24 |
| 3 | 82 ÷ 24 = 3 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 59 | 1003 |
| 37 and 15 | 555 |
| 92 and 160 | 3680 |
| 193 and 158 | 30494 |
| 25 and 140 | 700 |