Least Common Multiple (LCM) of 109 and 145
The least common multiple (LCM) of 109 and 145 is 15805.
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 109 and 145?
First, calculate the GCD of 109 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 145 = 0 remainder 109 |
| 2 | 145 ÷ 109 = 1 remainder 36 |
| 3 | 109 ÷ 36 = 3 remainder 1 |
| 4 | 36 ÷ 1 = 36 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 154 | 10318 |
| 100 and 112 | 2800 |
| 75 and 112 | 8400 |
| 68 and 19 | 1292 |
| 25 and 106 | 2650 |