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 |
|---|---|
| 134 and 17 | 2278 |
| 169 and 177 | 29913 |
| 197 and 123 | 24231 |
| 182 and 146 | 13286 |
| 57 and 186 | 3534 |