Least Common Multiple (LCM) of 173 and 123
The least common multiple (LCM) of 173 and 123 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 173 and 123?
First, calculate the GCD of 173 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 123 = 1 remainder 50 |
| 2 | 123 ÷ 50 = 2 remainder 23 |
| 3 | 50 ÷ 23 = 2 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 23 | 299 |
| 122 and 197 | 24034 |
| 164 and 155 | 25420 |
| 137 and 28 | 3836 |
| 183 and 120 | 7320 |