Least Common Multiple (LCM) of 111 and 31
The least common multiple (LCM) of 111 and 31 is 3441.
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 111 and 31?
First, calculate the GCD of 111 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 31 = 3 remainder 18 |
| 2 | 31 ÷ 18 = 1 remainder 13 |
| 3 | 18 ÷ 13 = 1 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 101 | 14241 |
| 162 and 149 | 24138 |
| 30 and 35 | 210 |
| 136 and 90 | 6120 |
| 118 and 156 | 9204 |