Least Common Multiple (LCM) of 106 and 140
The least common multiple (LCM) of 106 and 140 is 7420.
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 106 and 140?
First, calculate the GCD of 106 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 140 = 0 remainder 106 |
| 2 | 140 ÷ 106 = 1 remainder 34 |
| 3 | 106 ÷ 34 = 3 remainder 4 |
| 4 | 34 ÷ 4 = 8 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 100 | 1700 |
| 103 and 116 | 11948 |
| 123 and 12 | 492 |
| 177 and 144 | 8496 |
| 103 and 55 | 5665 |