Least Common Multiple (LCM) of 188 and 108
The least common multiple (LCM) of 188 and 108 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 188 and 108?
First, calculate the GCD of 188 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 108 = 1 remainder 80 |
| 2 | 108 ÷ 80 = 1 remainder 28 |
| 3 | 80 ÷ 28 = 2 remainder 24 |
| 4 | 28 ÷ 24 = 1 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 153 | 7038 |
| 81 and 24 | 648 |
| 59 and 87 | 5133 |
| 101 and 22 | 2222 |
| 188 and 159 | 29892 |