Least Common Multiple (LCM) of 20 and 69
The least common multiple (LCM) of 20 and 69 is 1380.
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 69?
First, calculate the GCD of 20 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 69 = 0 remainder 20 |
| 2 | 69 ÷ 20 = 3 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 |
|---|---|
| 25 and 84 | 2100 |
| 138 and 57 | 2622 |
| 163 and 45 | 7335 |
| 199 and 171 | 34029 |
| 111 and 146 | 16206 |