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 |
|---|---|
| 174 and 59 | 10266 |
| 37 and 189 | 6993 |
| 110 and 120 | 1320 |
| 77 and 87 | 6699 |
| 43 and 69 | 2967 |