Least Common Multiple (LCM) of 107 and 85
The least common multiple (LCM) of 107 and 85 is 9095.
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 85?
First, calculate the GCD of 107 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 85 = 1 remainder 22 |
| 2 | 85 ÷ 22 = 3 remainder 19 |
| 3 | 22 ÷ 19 = 1 remainder 3 |
| 4 | 19 ÷ 3 = 6 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 84 | 8148 |
| 104 and 197 | 20488 |
| 87 and 42 | 1218 |
| 169 and 128 | 21632 |
| 78 and 197 | 15366 |