Least Common Multiple (LCM) of 30 and 58
The least common multiple (LCM) of 30 and 58 is 870.
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 30 and 58?
First, calculate the GCD of 30 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 58 = 0 remainder 30 |
| 2 | 58 ÷ 30 = 1 remainder 28 |
| 3 | 30 ÷ 28 = 1 remainder 2 |
| 4 | 28 ÷ 2 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 150 | 4800 |
| 147 and 128 | 18816 |
| 134 and 39 | 5226 |
| 129 and 105 | 4515 |
| 196 and 14 | 196 |