Least Common Multiple (LCM) of 31 and 104
The least common multiple (LCM) of 31 and 104 is 3224.
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 104?
First, calculate the GCD of 31 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 104 = 0 remainder 31 |
| 2 | 104 ÷ 31 = 3 remainder 11 |
| 3 | 31 ÷ 11 = 2 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 45 | 6705 |
| 120 and 157 | 18840 |
| 171 and 84 | 4788 |
| 129 and 13 | 1677 |
| 114 and 140 | 7980 |