Least Common Multiple (LCM) of 67 and 184
The least common multiple (LCM) of 67 and 184 is 12328.
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 67 and 184?
First, calculate the GCD of 67 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 184 = 0 remainder 67 |
| 2 | 184 ÷ 67 = 2 remainder 50 |
| 3 | 67 ÷ 50 = 1 remainder 17 |
| 4 | 50 ÷ 17 = 2 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 53 | 9116 |
| 144 and 121 | 17424 |
| 138 and 21 | 966 |
| 148 and 29 | 4292 |
| 26 and 78 | 78 |