Least Common Multiple (LCM) of 188 and 102
The least common multiple (LCM) of 188 and 102 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 188 and 102?
First, calculate the GCD of 188 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 102 = 1 remainder 86 |
| 2 | 102 ÷ 86 = 1 remainder 16 |
| 3 | 86 ÷ 16 = 5 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 151 | 21895 |
| 142 and 81 | 11502 |
| 75 and 47 | 3525 |
| 47 and 74 | 3478 |
| 191 and 159 | 30369 |