Least Common Multiple (LCM) of 103 and 139
The least common multiple (LCM) of 103 and 139 is 14317.
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 139?
First, calculate the GCD of 103 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 139 = 0 remainder 103 |
| 2 | 139 ÷ 103 = 1 remainder 36 |
| 3 | 103 ÷ 36 = 2 remainder 31 |
| 4 | 36 ÷ 31 = 1 remainder 5 |
| 5 | 31 ÷ 5 = 6 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 68 | 4284 |
| 37 and 37 | 37 |
| 29 and 77 | 2233 |
| 149 and 138 | 20562 |
| 20 and 147 | 2940 |