Least Common Multiple (LCM) of 78 and 139
The least common multiple (LCM) of 78 and 139 is 10842.
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 139?
First, calculate the GCD of 78 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 139 = 0 remainder 78 |
| 2 | 139 ÷ 78 = 1 remainder 61 |
| 3 | 78 ÷ 61 = 1 remainder 17 |
| 4 | 61 ÷ 17 = 3 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 12 | 468 |
| 75 and 168 | 4200 |
| 164 and 179 | 29356 |
| 166 and 174 | 14442 |
| 144 and 153 | 2448 |