Least Common Multiple (LCM) of 77 and 114
The least common multiple (LCM) of 77 and 114 is 8778.
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 114?
First, calculate the GCD of 77 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 114 = 0 remainder 77 |
| 2 | 114 ÷ 77 = 1 remainder 37 |
| 3 | 77 ÷ 37 = 2 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 165 | 825 |
| 122 and 48 | 2928 |
| 56 and 184 | 1288 |
| 96 and 97 | 9312 |
| 195 and 63 | 4095 |