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 |
|---|---|
| 141 and 20 | 2820 |
| 82 and 42 | 1722 |
| 127 and 105 | 13335 |
| 10 and 194 | 970 |
| 31 and 83 | 2573 |