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 |
|---|---|
| 39 and 89 | 3471 |
| 98 and 176 | 8624 |
| 188 and 22 | 2068 |
| 160 and 109 | 17440 |
| 155 and 38 | 5890 |