Least Common Multiple (LCM) of 107 and 38
The least common multiple (LCM) of 107 and 38 is 4066.
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 107 and 38?
First, calculate the GCD of 107 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 38 = 2 remainder 31 |
| 2 | 38 ÷ 31 = 1 remainder 7 |
| 3 | 31 ÷ 7 = 4 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 106 | 5830 |
| 197 and 190 | 37430 |
| 105 and 54 | 1890 |
| 180 and 129 | 7740 |
| 148 and 109 | 16132 |