Least Common Multiple (LCM) of 78 and 178
The least common multiple (LCM) of 78 and 178 is 6942.
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 178?
First, calculate the GCD of 78 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 178 = 0 remainder 78 |
| 2 | 178 ÷ 78 = 2 remainder 22 |
| 3 | 78 ÷ 22 = 3 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 38 | 7182 |
| 78 and 41 | 3198 |
| 12 and 96 | 96 |
| 139 and 113 | 15707 |
| 102 and 174 | 2958 |