Least Common Multiple (LCM) of 103 and 174
The least common multiple (LCM) of 103 and 174 is 17922.
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 174?
First, calculate the GCD of 103 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 174 = 0 remainder 103 |
| 2 | 174 ÷ 103 = 1 remainder 71 |
| 3 | 103 ÷ 71 = 1 remainder 32 |
| 4 | 71 ÷ 32 = 2 remainder 7 |
| 5 | 32 ÷ 7 = 4 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 12 | 1524 |
| 186 and 172 | 15996 |
| 193 and 169 | 32617 |
| 160 and 157 | 25120 |
| 76 and 108 | 2052 |