Least Common Multiple (LCM) of 177 and 103
The least common multiple (LCM) of 177 and 103 is 18231.
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 103?
First, calculate the GCD of 177 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 103 = 1 remainder 74 |
| 2 | 103 ÷ 74 = 1 remainder 29 |
| 3 | 74 ÷ 29 = 2 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 30 | 210 |
| 143 and 162 | 23166 |
| 25 and 60 | 300 |
| 99 and 152 | 15048 |
| 35 and 30 | 210 |