Least Common Multiple (LCM) of 102 and 188
The least common multiple (LCM) of 102 and 188 is 9588.
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 102 and 188?
First, calculate the GCD of 102 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 188 = 0 remainder 102 |
| 2 | 188 ÷ 102 = 1 remainder 86 |
| 3 | 102 ÷ 86 = 1 remainder 16 |
| 4 | 86 ÷ 16 = 5 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 27 | 4968 |
| 109 and 30 | 3270 |
| 50 and 37 | 1850 |
| 58 and 85 | 4930 |
| 142 and 135 | 19170 |