Least Common Multiple (LCM) of 138 and 103
The least common multiple (LCM) of 138 and 103 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 138 and 103?
First, calculate the GCD of 138 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 103 = 1 remainder 35 |
| 2 | 103 ÷ 35 = 2 remainder 33 |
| 3 | 35 ÷ 33 = 1 remainder 2 |
| 4 | 33 ÷ 2 = 16 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 78 | 1326 |
| 181 and 113 | 20453 |
| 198 and 48 | 1584 |
| 110 and 84 | 4620 |
| 25 and 114 | 2850 |