Least Common Multiple (LCM) of 103 and 187
The least common multiple (LCM) of 103 and 187 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 103 and 187?
First, calculate the GCD of 103 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 187 = 0 remainder 103 |
| 2 | 187 ÷ 103 = 1 remainder 84 |
| 3 | 103 ÷ 84 = 1 remainder 19 |
| 4 | 84 ÷ 19 = 4 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 151 | 20687 |
| 78 and 161 | 12558 |
| 154 and 188 | 14476 |
| 51 and 51 | 51 |
| 135 and 160 | 4320 |