Least Common Multiple (LCM) of 78 and 167
The least common multiple (LCM) of 78 and 167 is 13026.
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 167?
First, calculate the GCD of 78 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 167 = 0 remainder 78 |
| 2 | 167 ÷ 78 = 2 remainder 11 |
| 3 | 78 ÷ 11 = 7 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 107 | 6099 |
| 43 and 123 | 5289 |
| 45 and 99 | 495 |
| 188 and 106 | 9964 |
| 164 and 131 | 21484 |