Least Common Multiple (LCM) of 114 and 107
The least common multiple (LCM) of 114 and 107 is 12198.
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 114 and 107?
First, calculate the GCD of 114 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 107 = 1 remainder 7 |
| 2 | 107 ÷ 7 = 15 remainder 2 |
| 3 | 7 ÷ 2 = 3 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 126 | 21294 |
| 132 and 133 | 17556 |
| 100 and 99 | 9900 |
| 81 and 130 | 10530 |
| 173 and 105 | 18165 |