Least Common Multiple (LCM) of 77 and 116
The least common multiple (LCM) of 77 and 116 is 8932.
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 116?
First, calculate the GCD of 77 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 116 = 0 remainder 77 |
| 2 | 116 ÷ 77 = 1 remainder 39 |
| 3 | 77 ÷ 39 = 1 remainder 38 |
| 4 | 39 ÷ 38 = 1 remainder 1 |
| 5 | 38 ÷ 1 = 38 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 17 | 2278 |
| 13 and 177 | 2301 |
| 44 and 168 | 1848 |
| 172 and 144 | 6192 |
| 109 and 12 | 1308 |