Least Common Multiple (LCM) of 78 and 170
The least common multiple (LCM) of 78 and 170 is 6630.
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 170?
First, calculate the GCD of 78 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 170 = 0 remainder 78 |
| 2 | 170 ÷ 78 = 2 remainder 14 |
| 3 | 78 ÷ 14 = 5 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 165 | 9735 |
| 126 and 182 | 1638 |
| 13 and 113 | 1469 |
| 100 and 168 | 4200 |
| 134 and 109 | 14606 |