Least Common Multiple (LCM) of 31 and 34
The least common multiple (LCM) of 31 and 34 is 1054.
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 34?
First, calculate the GCD of 31 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 34 = 0 remainder 31 |
| 2 | 34 ÷ 31 = 1 remainder 3 |
| 3 | 31 ÷ 3 = 10 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 126 | 10710 |
| 130 and 20 | 260 |
| 172 and 71 | 12212 |
| 100 and 22 | 1100 |
| 105 and 196 | 2940 |