Least Common Multiple (LCM) of 129 and 78
The least common multiple (LCM) of 129 and 78 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 129 and 78?
First, calculate the GCD of 129 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 78 = 1 remainder 51 |
| 2 | 78 ÷ 51 = 1 remainder 27 |
| 3 | 51 ÷ 27 = 1 remainder 24 |
| 4 | 27 ÷ 24 = 1 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 72 | 6552 |
| 37 and 74 | 74 |
| 31 and 69 | 2139 |
| 120 and 173 | 20760 |
| 191 and 155 | 29605 |