Least Common Multiple (LCM) of 107 and 184
The least common multiple (LCM) of 107 and 184 is 19688.
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 184?
First, calculate the GCD of 107 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 184 = 0 remainder 107 |
| 2 | 184 ÷ 107 = 1 remainder 77 |
| 3 | 107 ÷ 77 = 1 remainder 30 |
| 4 | 77 ÷ 30 = 2 remainder 17 |
| 5 | 30 ÷ 17 = 1 remainder 13 |
| 6 | 17 ÷ 13 = 1 remainder 4 |
| 7 | 13 ÷ 4 = 3 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 17 | 1632 |
| 48 and 80 | 240 |
| 20 and 68 | 340 |
| 18 and 112 | 1008 |
| 190 and 102 | 9690 |