Least Common Multiple (LCM) of 20 and 67
The least common multiple (LCM) of 20 and 67 is 1340.
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 67?
First, calculate the GCD of 20 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 67 = 0 remainder 20 |
| 2 | 67 ÷ 20 = 3 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 52 | 8268 |
| 122 and 171 | 20862 |
| 196 and 89 | 17444 |
| 65 and 122 | 7930 |
| 84 and 125 | 10500 |