Least Common Multiple (LCM) of 20 and 169
The least common multiple (LCM) of 20 and 169 is 3380.
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 169?
First, calculate the GCD of 20 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 169 = 0 remainder 20 |
| 2 | 169 ÷ 20 = 8 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 |
|---|---|
| 164 and 55 | 9020 |
| 20 and 98 | 980 |
| 65 and 91 | 455 |
| 41 and 34 | 1394 |
| 30 and 195 | 390 |