Least Common Multiple (LCM) of 105 and 177
The least common multiple (LCM) of 105 and 177 is 6195.
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 105 and 177?
First, calculate the GCD of 105 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 177 = 0 remainder 105 |
| 2 | 177 ÷ 105 = 1 remainder 72 |
| 3 | 105 ÷ 72 = 1 remainder 33 |
| 4 | 72 ÷ 33 = 2 remainder 6 |
| 5 | 33 ÷ 6 = 5 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 164 | 1476 |
| 53 and 58 | 3074 |
| 75 and 153 | 3825 |
| 39 and 167 | 6513 |
| 171 and 151 | 25821 |