Least Common Multiple (LCM) of 107 and 77
The least common multiple (LCM) of 107 and 77 is 8239.
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 77?
First, calculate the GCD of 107 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 77 = 1 remainder 30 |
| 2 | 77 ÷ 30 = 2 remainder 17 |
| 3 | 30 ÷ 17 = 1 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 126 | 22806 |
| 163 and 95 | 15485 |
| 134 and 29 | 3886 |
| 84 and 199 | 16716 |
| 149 and 168 | 25032 |