Least Common Multiple (LCM) of 178 and 78
The least common multiple (LCM) of 178 and 78 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 178 and 78?
First, calculate the GCD of 178 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 78 = 2 remainder 22 |
| 2 | 78 ÷ 22 = 3 remainder 12 |
| 3 | 22 ÷ 12 = 1 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 161 | 9499 |
| 16 and 173 | 2768 |
| 54 and 184 | 4968 |
| 129 and 72 | 3096 |
| 45 and 198 | 990 |