Least Common Multiple (LCM) of 103 and 145
The least common multiple (LCM) of 103 and 145 is 14935.
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 145?
First, calculate the GCD of 103 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 145 = 0 remainder 103 |
| 2 | 145 ÷ 103 = 1 remainder 42 |
| 3 | 103 ÷ 42 = 2 remainder 19 |
| 4 | 42 ÷ 19 = 2 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 182 | 24934 |
| 138 and 101 | 13938 |
| 156 and 137 | 21372 |
| 110 and 155 | 3410 |
| 136 and 193 | 26248 |