Least Common Multiple (LCM) of 187 and 103
The least common multiple (LCM) of 187 and 103 is 19261.
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 187 and 103?
First, calculate the GCD of 187 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 103 = 1 remainder 84 |
| 2 | 103 ÷ 84 = 1 remainder 19 |
| 3 | 84 ÷ 19 = 4 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 65 | 10855 |
| 135 and 42 | 1890 |
| 140 and 115 | 3220 |
| 69 and 22 | 1518 |
| 195 and 172 | 33540 |