Least Common Multiple (LCM) of 103 and 176
The least common multiple (LCM) of 103 and 176 is 18128.
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 176?
First, calculate the GCD of 103 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 176 = 0 remainder 103 |
| 2 | 176 ÷ 103 = 1 remainder 73 |
| 3 | 103 ÷ 73 = 1 remainder 30 |
| 4 | 73 ÷ 30 = 2 remainder 13 |
| 5 | 30 ÷ 13 = 2 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 93 | 930 |
| 186 and 168 | 5208 |
| 105 and 110 | 2310 |
| 150 and 115 | 3450 |
| 109 and 197 | 21473 |