Least Common Multiple (LCM) of 123 and 173
The least common multiple (LCM) of 123 and 173 is 21279.
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 173?
First, calculate the GCD of 123 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 173 = 0 remainder 123 |
| 2 | 173 ÷ 123 = 1 remainder 50 |
| 3 | 123 ÷ 50 = 2 remainder 23 |
| 4 | 50 ÷ 23 = 2 remainder 4 |
| 5 | 23 ÷ 4 = 5 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 12 | 1956 |
| 61 and 45 | 2745 |
| 128 and 135 | 17280 |
| 23 and 55 | 1265 |
| 85 and 33 | 2805 |