Least Common Multiple (LCM) of 31 and 184
The least common multiple (LCM) of 31 and 184 is 5704.
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 31 and 184?
First, calculate the GCD of 31 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 184 = 0 remainder 31 |
| 2 | 184 ÷ 31 = 5 remainder 29 |
| 3 | 31 ÷ 29 = 1 remainder 2 |
| 4 | 29 ÷ 2 = 14 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 25 | 1175 |
| 106 and 139 | 14734 |
| 42 and 172 | 3612 |
| 110 and 195 | 4290 |
| 17 and 63 | 1071 |