Least Common Multiple (LCM) of 78 and 164
The least common multiple (LCM) of 78 and 164 is 6396.
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 164?
First, calculate the GCD of 78 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 164 = 0 remainder 78 |
| 2 | 164 ÷ 78 = 2 remainder 8 |
| 3 | 78 ÷ 8 = 9 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 37 | 6549 |
| 169 and 163 | 27547 |
| 152 and 185 | 28120 |
| 131 and 111 | 14541 |
| 10 and 24 | 120 |