Least Common Multiple (LCM) of 58 and 78
The least common multiple (LCM) of 58 and 78 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 58 and 78?
First, calculate the GCD of 58 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 78 = 0 remainder 58 |
| 2 | 78 ÷ 58 = 1 remainder 20 |
| 3 | 58 ÷ 20 = 2 remainder 18 |
| 4 | 20 ÷ 18 = 1 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 100 | 3700 |
| 107 and 192 | 20544 |
| 101 and 154 | 15554 |
| 40 and 53 | 2120 |
| 168 and 172 | 7224 |