Least Common Multiple (LCM) of 188 and 103
The least common multiple (LCM) of 188 and 103 is 19364.
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 103?
First, calculate the GCD of 188 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 103 = 1 remainder 85 |
| 2 | 103 ÷ 85 = 1 remainder 18 |
| 3 | 85 ÷ 18 = 4 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 36 | 144 |
| 78 and 36 | 468 |
| 131 and 200 | 26200 |
| 103 and 35 | 3605 |
| 75 and 65 | 975 |