Least Common Multiple (LCM) of 103 and 177
The least common multiple (LCM) of 103 and 177 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 103 and 177?
First, calculate the GCD of 103 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 177 = 0 remainder 103 |
| 2 | 177 ÷ 103 = 1 remainder 74 |
| 3 | 103 ÷ 74 = 1 remainder 29 |
| 4 | 74 ÷ 29 = 2 remainder 16 |
| 5 | 29 ÷ 16 = 1 remainder 13 |
| 6 | 16 ÷ 13 = 1 remainder 3 |
| 7 | 13 ÷ 3 = 4 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 153 | 918 |
| 181 and 84 | 15204 |
| 175 and 56 | 1400 |
| 156 and 69 | 3588 |
| 198 and 199 | 39402 |