Least Common Multiple (LCM) of 114 and 173
The least common multiple (LCM) of 114 and 173 is 19722.
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 114 and 173?
First, calculate the GCD of 114 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 173 = 0 remainder 114 |
| 2 | 173 ÷ 114 = 1 remainder 59 |
| 3 | 114 ÷ 59 = 1 remainder 55 |
| 4 | 59 ÷ 55 = 1 remainder 4 |
| 5 | 55 ÷ 4 = 13 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 174 | 10614 |
| 125 and 44 | 5500 |
| 194 and 189 | 36666 |
| 42 and 176 | 3696 |
| 196 and 104 | 5096 |