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 |
|---|---|
| 112 and 172 | 4816 |
| 196 and 94 | 9212 |
| 45 and 92 | 4140 |
| 192 and 166 | 15936 |
| 111 and 82 | 9102 |