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 |
|---|---|
| 60 and 80 | 240 |
| 153 and 173 | 26469 |
| 126 and 92 | 5796 |
| 105 and 153 | 5355 |
| 188 and 100 | 4700 |