Least Common Multiple (LCM) of 58 and 104
The least common multiple (LCM) of 58 and 104 is 3016.
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 104?
First, calculate the GCD of 58 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 104 = 0 remainder 58 |
| 2 | 104 ÷ 58 = 1 remainder 46 |
| 3 | 58 ÷ 46 = 1 remainder 12 |
| 4 | 46 ÷ 12 = 3 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 116 | 11716 |
| 74 and 42 | 1554 |
| 178 and 134 | 11926 |
| 162 and 142 | 11502 |
| 135 and 91 | 12285 |