Least Common Multiple (LCM) of 101 and 177
The least common multiple (LCM) of 101 and 177 is 17877.
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 101 and 177?
First, calculate the GCD of 101 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 177 = 0 remainder 101 |
| 2 | 177 ÷ 101 = 1 remainder 76 |
| 3 | 101 ÷ 76 = 1 remainder 25 |
| 4 | 76 ÷ 25 = 3 remainder 1 |
| 5 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 109 | 19402 |
| 109 and 169 | 18421 |
| 199 and 49 | 9751 |
| 178 and 129 | 22962 |
| 153 and 42 | 2142 |