Least Common Multiple (LCM) of 110 and 58
The least common multiple (LCM) of 110 and 58 is 3190.
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 110 and 58?
First, calculate the GCD of 110 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 58 = 1 remainder 52 |
| 2 | 58 ÷ 52 = 1 remainder 6 |
| 3 | 52 ÷ 6 = 8 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 19 | 133 |
| 41 and 146 | 5986 |
| 21 and 112 | 336 |
| 193 and 161 | 31073 |
| 87 and 117 | 3393 |