Least Common Multiple (LCM) of 78 and 131
The least common multiple (LCM) of 78 and 131 is 10218.
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 131?
First, calculate the GCD of 78 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 131 = 0 remainder 78 |
| 2 | 131 ÷ 78 = 1 remainder 53 |
| 3 | 78 ÷ 53 = 1 remainder 25 |
| 4 | 53 ÷ 25 = 2 remainder 3 |
| 5 | 25 ÷ 3 = 8 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 134 | 25326 |
| 121 and 190 | 22990 |
| 24 and 31 | 744 |
| 153 and 26 | 3978 |
| 116 and 140 | 4060 |