Least Common Multiple (LCM) of 78 and 83
The least common multiple (LCM) of 78 and 83 is 6474.
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 83?
First, calculate the GCD of 78 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 83 = 0 remainder 78 |
| 2 | 83 ÷ 78 = 1 remainder 5 |
| 3 | 78 ÷ 5 = 15 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 24 | 2424 |
| 142 and 67 | 9514 |
| 197 and 160 | 31520 |
| 61 and 176 | 10736 |
| 182 and 25 | 4550 |