Least Common Multiple (LCM) of 103 and 138
The least common multiple (LCM) of 103 and 138 is 14214.
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 138?
First, calculate the GCD of 103 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 138 = 0 remainder 103 |
| 2 | 138 ÷ 103 = 1 remainder 35 |
| 3 | 103 ÷ 35 = 2 remainder 33 |
| 4 | 35 ÷ 33 = 1 remainder 2 |
| 5 | 33 ÷ 2 = 16 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 65 | 12805 |
| 15 and 115 | 345 |
| 144 and 159 | 7632 |
| 121 and 19 | 2299 |
| 65 and 129 | 8385 |