Least Common Multiple (LCM) of 45 and 173
The least common multiple (LCM) of 45 and 173 is 7785.
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 45 and 173?
First, calculate the GCD of 45 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 173 = 0 remainder 45 |
| 2 | 173 ÷ 45 = 3 remainder 38 |
| 3 | 45 ÷ 38 = 1 remainder 7 |
| 4 | 38 ÷ 7 = 5 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 125 | 2750 |
| 77 and 181 | 13937 |
| 129 and 145 | 18705 |
| 148 and 148 | 148 |
| 148 and 17 | 2516 |