Least Common Multiple (LCM) of 105 and 58
The least common multiple (LCM) of 105 and 58 is 6090.
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 105 and 58?
First, calculate the GCD of 105 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 58 = 1 remainder 47 |
| 2 | 58 ÷ 47 = 1 remainder 11 |
| 3 | 47 ÷ 11 = 4 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 141 | 1833 |
| 65 and 120 | 1560 |
| 80 and 107 | 8560 |
| 41 and 103 | 4223 |
| 79 and 49 | 3871 |