Least Common Multiple (LCM) of 105 and 145
The least common multiple (LCM) of 105 and 145 is 3045.
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 105 and 145?
First, calculate the GCD of 105 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 145 = 0 remainder 105 |
| 2 | 145 ÷ 105 = 1 remainder 40 |
| 3 | 105 ÷ 40 = 2 remainder 25 |
| 4 | 40 ÷ 25 = 1 remainder 15 |
| 5 | 25 ÷ 15 = 1 remainder 10 |
| 6 | 15 ÷ 10 = 1 remainder 5 |
| 7 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 191 | 13561 |
| 99 and 49 | 4851 |
| 186 and 116 | 10788 |
| 123 and 137 | 16851 |
| 45 and 34 | 1530 |