Least Common Multiple (LCM) of 38 and 173
The least common multiple (LCM) of 38 and 173 is 6574.
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 38 and 173?
First, calculate the GCD of 38 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 173 = 0 remainder 38 |
| 2 | 173 ÷ 38 = 4 remainder 21 |
| 3 | 38 ÷ 21 = 1 remainder 17 |
| 4 | 21 ÷ 17 = 1 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 105 | 2415 |
| 18 and 95 | 1710 |
| 148 and 163 | 24124 |
| 63 and 32 | 2016 |
| 97 and 27 | 2619 |