Least Common Multiple (LCM) of 14 and 145
The least common multiple (LCM) of 14 and 145 is 2030.
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 14 and 145?
First, calculate the GCD of 14 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 145 = 0 remainder 14 |
| 2 | 145 ÷ 14 = 10 remainder 5 |
| 3 | 14 ÷ 5 = 2 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 39 | 4251 |
| 146 and 154 | 11242 |
| 171 and 175 | 29925 |
| 200 and 111 | 22200 |
| 135 and 139 | 18765 |