Least Common Multiple (LCM) of 77 and 108
The least common multiple (LCM) of 77 and 108 is 8316.
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 77 and 108?
First, calculate the GCD of 77 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 108 = 0 remainder 77 |
| 2 | 108 ÷ 77 = 1 remainder 31 |
| 3 | 77 ÷ 31 = 2 remainder 15 |
| 4 | 31 ÷ 15 = 2 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 80 | 14160 |
| 90 and 39 | 1170 |
| 49 and 112 | 784 |
| 168 and 195 | 10920 |
| 53 and 78 | 4134 |