Least Common Multiple (LCM) of 145 and 107
The least common multiple (LCM) of 145 and 107 is 15515.
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 107?
First, calculate the GCD of 145 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 107 = 1 remainder 38 |
| 2 | 107 ÷ 38 = 2 remainder 31 |
| 3 | 38 ÷ 31 = 1 remainder 7 |
| 4 | 31 ÷ 7 = 4 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 168 | 4200 |
| 191 and 195 | 37245 |
| 113 and 17 | 1921 |
| 11 and 130 | 1430 |
| 178 and 188 | 16732 |