Least Common Multiple (LCM) of 34 and 184
The least common multiple (LCM) of 34 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 34 and 184?
First, calculate the GCD of 34 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 184 = 0 remainder 34 |
| 2 | 184 ÷ 34 = 5 remainder 14 |
| 3 | 34 ÷ 14 = 2 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 200 | 600 |
| 179 and 67 | 11993 |
| 38 and 125 | 4750 |
| 17 and 165 | 2805 |
| 55 and 29 | 1595 |