Least Common Multiple (LCM) of 103 and 146
The least common multiple (LCM) of 103 and 146 is 15038.
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 146?
First, calculate the GCD of 103 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 146 = 0 remainder 103 |
| 2 | 146 ÷ 103 = 1 remainder 43 |
| 3 | 103 ÷ 43 = 2 remainder 17 |
| 4 | 43 ÷ 17 = 2 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 78 | 468 |
| 48 and 138 | 1104 |
| 148 and 46 | 3404 |
| 199 and 68 | 13532 |
| 182 and 45 | 8190 |