Least Common Multiple (LCM) of 20 and 114
The least common multiple (LCM) of 20 and 114 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 20 and 114?
First, calculate the GCD of 20 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 114 = 0 remainder 20 |
| 2 | 114 ÷ 20 = 5 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 69 | 828 |
| 55 and 142 | 7810 |
| 27 and 67 | 1809 |
| 193 and 39 | 7527 |
| 122 and 36 | 2196 |