Least Common Multiple (LCM) of 78 and 129
The least common multiple (LCM) of 78 and 129 is 3354.
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 129?
First, calculate the GCD of 78 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 129 = 0 remainder 78 |
| 2 | 129 ÷ 78 = 1 remainder 51 |
| 3 | 78 ÷ 51 = 1 remainder 27 |
| 4 | 51 ÷ 27 = 1 remainder 24 |
| 5 | 27 ÷ 24 = 1 remainder 3 |
| 6 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 19 | 2071 |
| 196 and 123 | 24108 |
| 152 and 130 | 9880 |
| 40 and 149 | 5960 |
| 135 and 135 | 135 |