Least Common Multiple (LCM) of 20 and 173
The least common multiple (LCM) of 20 and 173 is 3460.
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 173?
First, calculate the GCD of 20 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 173 = 0 remainder 20 |
| 2 | 173 ÷ 20 = 8 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 155 | 2015 |
| 40 and 91 | 3640 |
| 112 and 61 | 6832 |
| 80 and 186 | 7440 |
| 198 and 71 | 14058 |