Least Common Multiple (LCM) of 116 and 77
The least common multiple (LCM) of 116 and 77 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 116 and 77?
First, calculate the GCD of 116 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 77 = 1 remainder 39 |
| 2 | 77 ÷ 39 = 1 remainder 38 |
| 3 | 39 ÷ 38 = 1 remainder 1 |
| 4 | 38 ÷ 1 = 38 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 108 | 8316 |
| 31 and 20 | 620 |
| 85 and 106 | 9010 |
| 131 and 176 | 23056 |
| 16 and 186 | 1488 |