Least Common Multiple (LCM) of 31 and 112
The least common multiple (LCM) of 31 and 112 is 3472.
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 112?
First, calculate the GCD of 31 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 112 = 0 remainder 31 |
| 2 | 112 ÷ 31 = 3 remainder 19 |
| 3 | 31 ÷ 19 = 1 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 136 | 17272 |
| 116 and 188 | 5452 |
| 80 and 90 | 720 |
| 148 and 197 | 29156 |
| 103 and 81 | 8343 |