Least Common Multiple (LCM) of 108 and 188
The least common multiple (LCM) of 108 and 188 is 5076.
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 108 and 188?
First, calculate the GCD of 108 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 188 = 0 remainder 108 |
| 2 | 188 ÷ 108 = 1 remainder 80 |
| 3 | 108 ÷ 80 = 1 remainder 28 |
| 4 | 80 ÷ 28 = 2 remainder 24 |
| 5 | 28 ÷ 24 = 1 remainder 4 |
| 6 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 199 | 15920 |
| 122 and 175 | 21350 |
| 21 and 185 | 3885 |
| 133 and 34 | 4522 |
| 106 and 126 | 6678 |