Least Common Multiple (LCM) of 107 and 102
The least common multiple (LCM) of 107 and 102 is 10914.
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 102?
First, calculate the GCD of 107 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 102 = 1 remainder 5 |
| 2 | 102 ÷ 5 = 20 remainder 2 |
| 3 | 5 ÷ 2 = 2 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 80 | 9040 |
| 38 and 129 | 4902 |
| 140 and 101 | 14140 |
| 89 and 17 | 1513 |
| 199 and 145 | 28855 |