Least Common Multiple (LCM) of 174 and 103
The least common multiple (LCM) of 174 and 103 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 174 and 103?
First, calculate the GCD of 174 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 103 = 1 remainder 71 |
| 2 | 103 ÷ 71 = 1 remainder 32 |
| 3 | 71 ÷ 32 = 2 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 76 | 7828 |
| 172 and 45 | 7740 |
| 76 and 18 | 684 |
| 148 and 36 | 1332 |
| 106 and 96 | 5088 |