Least Common Multiple (LCM) of 103 and 178
The least common multiple (LCM) of 103 and 178 is 18334.
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 178?
First, calculate the GCD of 103 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 178 = 0 remainder 103 |
| 2 | 178 ÷ 103 = 1 remainder 75 |
| 3 | 103 ÷ 75 = 1 remainder 28 |
| 4 | 75 ÷ 28 = 2 remainder 19 |
| 5 | 28 ÷ 19 = 1 remainder 9 |
| 6 | 19 ÷ 9 = 2 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 183 | 2013 |
| 101 and 199 | 20099 |
| 130 and 109 | 14170 |
| 145 and 23 | 3335 |
| 157 and 146 | 22922 |