Least Common Multiple (LCM) of 31 and 188
The least common multiple (LCM) of 31 and 188 is 5828.
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 188?
First, calculate the GCD of 31 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 188 = 0 remainder 31 |
| 2 | 188 ÷ 31 = 6 remainder 2 |
| 3 | 31 ÷ 2 = 15 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 85 | 5355 |
| 120 and 35 | 840 |
| 113 and 150 | 16950 |
| 159 and 70 | 11130 |
| 168 and 168 | 168 |