Least Common Multiple (LCM) of 46 and 173
The least common multiple (LCM) of 46 and 173 is 7958.
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 46 and 173?
First, calculate the GCD of 46 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 173 = 0 remainder 46 |
| 2 | 173 ÷ 46 = 3 remainder 35 |
| 3 | 46 ÷ 35 = 1 remainder 11 |
| 4 | 35 ÷ 11 = 3 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 105 | 2100 |
| 134 and 157 | 21038 |
| 143 and 156 | 1716 |
| 175 and 28 | 700 |
| 83 and 27 | 2241 |