Least Common Multiple (LCM) of 30 and 31
The least common multiple (LCM) of 30 and 31 is 930.
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 30 and 31?
First, calculate the GCD of 30 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 31 = 0 remainder 30 |
| 2 | 31 ÷ 30 = 1 remainder 1 |
| 3 | 30 ÷ 1 = 30 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 175 | 3325 |
| 162 and 16 | 1296 |
| 169 and 89 | 15041 |
| 17 and 155 | 2635 |
| 191 and 138 | 26358 |