Least Common Multiple (LCM) of 114 and 30
The least common multiple (LCM) of 114 and 30 is 570.
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 114 and 30?
First, calculate the GCD of 114 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 30 = 3 remainder 24 |
| 2 | 30 ÷ 24 = 1 remainder 6 |
| 3 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 89 | 178 |
| 95 and 20 | 380 |
| 158 and 137 | 21646 |
| 188 and 18 | 1692 |
| 140 and 46 | 3220 |