Least Common Multiple (LCM) of 177 and 106
The least common multiple (LCM) of 177 and 106 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 177 and 106?
First, calculate the GCD of 177 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 106 = 1 remainder 71 |
| 2 | 106 ÷ 71 = 1 remainder 35 |
| 3 | 71 ÷ 35 = 2 remainder 1 |
| 4 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 174 | 27318 |
| 47 and 89 | 4183 |
| 165 and 109 | 17985 |
| 162 and 193 | 31266 |
| 149 and 121 | 18029 |