Least Common Multiple (LCM) of 78 and 173
The least common multiple (LCM) of 78 and 173 is 13494.
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 78 and 173?
First, calculate the GCD of 78 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 173 = 0 remainder 78 |
| 2 | 173 ÷ 78 = 2 remainder 17 |
| 3 | 78 ÷ 17 = 4 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 16 | 1744 |
| 125 and 183 | 22875 |
| 61 and 193 | 11773 |
| 100 and 196 | 4900 |
| 189 and 119 | 3213 |