Least Common Multiple (LCM) of 58 and 112
The least common multiple (LCM) of 58 and 112 is 3248.
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 112?
First, calculate the GCD of 58 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 112 = 0 remainder 58 |
| 2 | 112 ÷ 58 = 1 remainder 54 |
| 3 | 58 ÷ 54 = 1 remainder 4 |
| 4 | 54 ÷ 4 = 13 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 33 | 5511 |
| 108 and 90 | 540 |
| 13 and 105 | 1365 |
| 10 and 58 | 290 |
| 113 and 52 | 5876 |