Least Common Multiple (LCM) of 68 and 184
The least common multiple (LCM) of 68 and 184 is 3128.
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 68 and 184?
First, calculate the GCD of 68 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 184 = 0 remainder 68 |
| 2 | 184 ÷ 68 = 2 remainder 48 |
| 3 | 68 ÷ 48 = 1 remainder 20 |
| 4 | 48 ÷ 20 = 2 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 69 | 2139 |
| 178 and 139 | 24742 |
| 46 and 198 | 4554 |
| 170 and 95 | 3230 |
| 10 and 18 | 90 |