Least Common Multiple (LCM) of 31 and 185
The least common multiple (LCM) of 31 and 185 is 5735.
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 185?
First, calculate the GCD of 31 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 185 = 0 remainder 31 |
| 2 | 185 ÷ 31 = 5 remainder 30 |
| 3 | 31 ÷ 30 = 1 remainder 1 |
| 4 | 30 ÷ 1 = 30 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 118 | 13806 |
| 61 and 106 | 6466 |
| 145 and 71 | 10295 |
| 185 and 133 | 24605 |
| 38 and 89 | 3382 |