Least Common Multiple (LCM) of 108 and 184
The least common multiple (LCM) of 108 and 184 is 4968.
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 108 and 184?
First, calculate the GCD of 108 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 184 = 0 remainder 108 |
| 2 | 184 ÷ 108 = 1 remainder 76 |
| 3 | 108 ÷ 76 = 1 remainder 32 |
| 4 | 76 ÷ 32 = 2 remainder 12 |
| 5 | 32 ÷ 12 = 2 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 71 | 12638 |
| 165 and 116 | 19140 |
| 52 and 109 | 5668 |
| 185 and 87 | 16095 |
| 125 and 96 | 12000 |