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 |
|---|---|
| 15 and 192 | 960 |
| 106 and 36 | 1908 |
| 18 and 88 | 792 |
| 17 and 39 | 663 |
| 169 and 66 | 11154 |