Least Common Multiple (LCM) of 31 and 41
The least common multiple (LCM) of 31 and 41 is 1271.
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 41?
First, calculate the GCD of 31 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 41 = 0 remainder 31 |
| 2 | 41 ÷ 31 = 1 remainder 10 |
| 3 | 31 ÷ 10 = 3 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 126 | 1638 |
| 184 and 35 | 6440 |
| 185 and 105 | 3885 |
| 125 and 168 | 21000 |
| 122 and 128 | 7808 |