Least Common Multiple (LCM) of 78 and 67
The least common multiple (LCM) of 78 and 67 is 5226.
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 67?
First, calculate the GCD of 78 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 67 = 1 remainder 11 |
| 2 | 67 ÷ 11 = 6 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 44 | 704 |
| 65 and 175 | 2275 |
| 166 and 133 | 22078 |
| 122 and 75 | 9150 |
| 93 and 186 | 186 |