Least Common Multiple (LCM) of 114 and 20
The least common multiple (LCM) of 114 and 20 is 1140.
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 20?
First, calculate the GCD of 114 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 20 = 5 remainder 14 |
| 2 | 20 ÷ 14 = 1 remainder 6 |
| 3 | 14 ÷ 6 = 2 remainder 2 |
| 4 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 47 | 7473 |
| 24 and 54 | 216 |
| 171 and 17 | 2907 |
| 42 and 81 | 1134 |
| 54 and 102 | 918 |