Least Common Multiple (LCM) of 20 and 49
The least common multiple (LCM) of 20 and 49 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 49?
First, calculate the GCD of 20 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 49 = 0 remainder 20 |
| 2 | 49 ÷ 20 = 2 remainder 9 |
| 3 | 20 ÷ 9 = 2 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 109 | 20819 |
| 163 and 172 | 28036 |
| 73 and 196 | 14308 |
| 179 and 56 | 10024 |
| 164 and 108 | 4428 |