Least Common Multiple (LCM) of 140 and 107
The least common multiple (LCM) of 140 and 107 is 14980.
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 140 and 107?
First, calculate the GCD of 140 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 107 = 1 remainder 33 |
| 2 | 107 ÷ 33 = 3 remainder 8 |
| 3 | 33 ÷ 8 = 4 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 109 | 21037 |
| 143 and 145 | 20735 |
| 58 and 188 | 5452 |
| 100 and 103 | 10300 |
| 134 and 142 | 9514 |