Least Common Multiple (LCM) of 18 and 107
The least common multiple (LCM) of 18 and 107 is 1926.
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 18 and 107?
First, calculate the GCD of 18 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 107 = 0 remainder 18 |
| 2 | 107 ÷ 18 = 5 remainder 17 |
| 3 | 18 ÷ 17 = 1 remainder 1 |
| 4 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 79 | 1343 |
| 80 and 67 | 5360 |
| 189 and 49 | 1323 |
| 51 and 86 | 4386 |
| 180 and 25 | 900 |