Least Common Multiple (LCM) of 139 and 78
The least common multiple (LCM) of 139 and 78 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 139 and 78?
First, calculate the GCD of 139 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 78 = 1 remainder 61 |
| 2 | 78 ÷ 61 = 1 remainder 17 |
| 3 | 61 ÷ 17 = 3 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 114 | 4902 |
| 41 and 73 | 2993 |
| 198 and 114 | 3762 |
| 199 and 58 | 11542 |
| 17 and 122 | 2074 |