Least Common Multiple (LCM) of 83 and 184
The least common multiple (LCM) of 83 and 184 is 15272.
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 83 and 184?
First, calculate the GCD of 83 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 184 = 0 remainder 83 |
| 2 | 184 ÷ 83 = 2 remainder 18 |
| 3 | 83 ÷ 18 = 4 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 187 | 34408 |
| 147 and 23 | 3381 |
| 11 and 51 | 561 |
| 27 and 40 | 1080 |
| 200 and 109 | 21800 |