Least Common Multiple (LCM) of 31 and 109
The least common multiple (LCM) of 31 and 109 is 3379.
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 109?
First, calculate the GCD of 31 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 109 = 0 remainder 31 |
| 2 | 109 ÷ 31 = 3 remainder 16 |
| 3 | 31 ÷ 16 = 1 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 48 | 816 |
| 137 and 195 | 26715 |
| 12 and 10 | 60 |
| 56 and 125 | 7000 |
| 171 and 148 | 25308 |