Least Common Multiple (LCM) of 20 and 28
The least common multiple (LCM) of 20 and 28 is 140.
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 28?
First, calculate the GCD of 20 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 28 = 0 remainder 20 |
| 2 | 28 ÷ 20 = 1 remainder 8 |
| 3 | 20 ÷ 8 = 2 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 37 | 4292 |
| 188 and 180 | 8460 |
| 53 and 66 | 3498 |
| 144 and 100 | 3600 |
| 65 and 153 | 9945 |