Least Common Multiple (LCM) of 123 and 174
The least common multiple (LCM) of 123 and 174 is 7134.
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 123 and 174?
First, calculate the GCD of 123 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 174 = 0 remainder 123 |
| 2 | 174 ÷ 123 = 1 remainder 51 |
| 3 | 123 ÷ 51 = 2 remainder 21 |
| 4 | 51 ÷ 21 = 2 remainder 9 |
| 5 | 21 ÷ 9 = 2 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 157 | 23079 |
| 193 and 168 | 32424 |
| 20 and 15 | 60 |
| 71 and 82 | 5822 |
| 101 and 159 | 16059 |