Least Common Multiple (LCM) of 78 and 58
The least common multiple (LCM) of 78 and 58 is 2262.
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 58?
First, calculate the GCD of 78 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 58 = 1 remainder 20 |
| 2 | 58 ÷ 20 = 2 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 185 | 19795 |
| 40 and 129 | 5160 |
| 76 and 116 | 2204 |
| 98 and 132 | 6468 |
| 91 and 189 | 2457 |