Least Common Multiple (LCM) of 58 and 103
The least common multiple (LCM) of 58 and 103 is 5974.
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 103?
First, calculate the GCD of 58 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 103 = 0 remainder 58 |
| 2 | 103 ÷ 58 = 1 remainder 45 |
| 3 | 58 ÷ 45 = 1 remainder 13 |
| 4 | 45 ÷ 13 = 3 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 153 | 30141 |
| 128 and 126 | 8064 |
| 162 and 177 | 9558 |
| 86 and 42 | 1806 |
| 93 and 64 | 5952 |