Least Common Multiple (LCM) of 145 and 103
The least common multiple (LCM) of 145 and 103 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 145 and 103?
First, calculate the GCD of 145 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 103 = 1 remainder 42 |
| 2 | 103 ÷ 42 = 2 remainder 19 |
| 3 | 42 ÷ 19 = 2 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 156 | 156 |
| 176 and 45 | 7920 |
| 101 and 131 | 13231 |
| 70 and 132 | 4620 |
| 97 and 58 | 5626 |