Least Common Multiple (LCM) of 174 and 123
The least common multiple (LCM) of 174 and 123 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 174 and 123?
First, calculate the GCD of 174 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 123 = 1 remainder 51 |
| 2 | 123 ÷ 51 = 2 remainder 21 |
| 3 | 51 ÷ 21 = 2 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 144 | 3024 |
| 20 and 40 | 40 |
| 117 and 93 | 3627 |
| 52 and 118 | 3068 |
| 65 and 58 | 3770 |