Least Common Multiple (LCM) of 31 and 108
The least common multiple (LCM) of 31 and 108 is 3348.
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 108?
First, calculate the GCD of 31 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 108 = 0 remainder 31 |
| 2 | 108 ÷ 31 = 3 remainder 15 |
| 3 | 31 ÷ 15 = 2 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 25 | 2050 |
| 52 and 179 | 9308 |
| 184 and 17 | 3128 |
| 179 and 192 | 34368 |
| 51 and 89 | 4539 |