Least Common Multiple (LCM) of 77 and 106
The least common multiple (LCM) of 77 and 106 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 77 and 106?
First, calculate the GCD of 77 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 106 = 0 remainder 77 |
| 2 | 106 ÷ 77 = 1 remainder 29 |
| 3 | 77 ÷ 29 = 2 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 14 | 742 |
| 40 and 98 | 1960 |
| 33 and 109 | 3597 |
| 137 and 35 | 4795 |
| 176 and 127 | 22352 |