Least Common Multiple (LCM) of 103 and 189
The least common multiple (LCM) of 103 and 189 is 19467.
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 189?
First, calculate the GCD of 103 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 189 = 0 remainder 103 |
| 2 | 189 ÷ 103 = 1 remainder 86 |
| 3 | 103 ÷ 86 = 1 remainder 17 |
| 4 | 86 ÷ 17 = 5 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 108 | 3348 |
| 138 and 30 | 690 |
| 28 and 27 | 756 |
| 82 and 146 | 5986 |
| 157 and 122 | 19154 |