Least Common Multiple (LCM) of 34 and 83
The least common multiple (LCM) of 34 and 83 is 2822.
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 83?
First, calculate the GCD of 34 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 83 = 0 remainder 34 |
| 2 | 83 ÷ 34 = 2 remainder 15 |
| 3 | 34 ÷ 15 = 2 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 184 | 1288 |
| 182 and 183 | 33306 |
| 159 and 135 | 7155 |
| 135 and 85 | 2295 |
| 88 and 24 | 264 |