Least Common Multiple (LCM) of 107 and 61
The least common multiple (LCM) of 107 and 61 is 6527.
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 61?
First, calculate the GCD of 107 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 61 = 1 remainder 46 |
| 2 | 61 ÷ 46 = 1 remainder 15 |
| 3 | 46 ÷ 15 = 3 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 78 | 1950 |
| 196 and 171 | 33516 |
| 17 and 16 | 272 |
| 179 and 55 | 9845 |
| 31 and 13 | 403 |