Least Common Multiple (LCM) of 106 and 77
The least common multiple (LCM) of 106 and 77 is 8162.
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 106 and 77?
First, calculate the GCD of 106 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 77 = 1 remainder 29 |
| 2 | 77 ÷ 29 = 2 remainder 19 |
| 3 | 29 ÷ 19 = 1 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 199 | 35024 |
| 25 and 67 | 1675 |
| 23 and 177 | 4071 |
| 88 and 124 | 2728 |
| 174 and 53 | 9222 |