Least Common Multiple (LCM) of 107 and 114
The least common multiple (LCM) of 107 and 114 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 107 and 114?
First, calculate the GCD of 107 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 114 = 0 remainder 107 |
| 2 | 114 ÷ 107 = 1 remainder 7 |
| 3 | 107 ÷ 7 = 15 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 112 | 1456 |
| 12 and 125 | 1500 |
| 128 and 141 | 18048 |
| 142 and 19 | 2698 |
| 153 and 71 | 10863 |