Least Common Multiple (LCM) of 102 and 77
The least common multiple (LCM) of 102 and 77 is 7854.
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 102 and 77?
First, calculate the GCD of 102 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 77 = 1 remainder 25 |
| 2 | 77 ÷ 25 = 3 remainder 2 |
| 3 | 25 ÷ 2 = 12 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 79 | 8295 |
| 168 and 182 | 2184 |
| 118 and 41 | 4838 |
| 70 and 33 | 2310 |
| 30 and 197 | 5910 |