Least Common Multiple (LCM) of 106 and 177
The least common multiple (LCM) of 106 and 177 is 18762.
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 177?
First, calculate the GCD of 106 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 177 = 0 remainder 106 |
| 2 | 177 ÷ 106 = 1 remainder 71 |
| 3 | 106 ÷ 71 = 1 remainder 35 |
| 4 | 71 ÷ 35 = 2 remainder 1 |
| 5 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 67 | 11591 |
| 23 and 110 | 2530 |
| 21 and 63 | 63 |
| 82 and 133 | 10906 |
| 50 and 129 | 6450 |