Least Common Multiple (LCM) of 20 and 196
The least common multiple (LCM) of 20 and 196 is 980.
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 196?
First, calculate the GCD of 20 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 196 = 0 remainder 20 |
| 2 | 196 ÷ 20 = 9 remainder 16 |
| 3 | 20 ÷ 16 = 1 remainder 4 |
| 4 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 128 | 25216 |
| 110 and 171 | 18810 |
| 51 and 154 | 7854 |
| 57 and 65 | 3705 |
| 113 and 100 | 11300 |