Least Common Multiple (LCM) of 107 and 20
The least common multiple (LCM) of 107 and 20 is 2140.
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 20?
First, calculate the GCD of 107 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 20 = 5 remainder 7 |
| 2 | 20 ÷ 7 = 2 remainder 6 |
| 3 | 7 ÷ 6 = 1 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 75 | 1650 |
| 138 and 124 | 8556 |
| 77 and 127 | 9779 |
| 175 and 168 | 4200 |
| 180 and 74 | 6660 |