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 |
|---|---|
| 49 and 158 | 7742 |
| 190 and 71 | 13490 |
| 141 and 154 | 21714 |
| 144 and 181 | 26064 |
| 116 and 124 | 3596 |