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 |
|---|---|
| 176 and 107 | 18832 |
| 43 and 71 | 3053 |
| 90 and 19 | 1710 |
| 128 and 199 | 25472 |
| 122 and 166 | 10126 |