Least Common Multiple (LCM) of 173 and 100
The least common multiple (LCM) of 173 and 100 is 17300.
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 173 and 100?
First, calculate the GCD of 173 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 100 = 1 remainder 73 |
| 2 | 100 ÷ 73 = 1 remainder 27 |
| 3 | 73 ÷ 27 = 2 remainder 19 |
| 4 | 27 ÷ 19 = 1 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 98 | 18130 |
| 39 and 24 | 312 |
| 97 and 199 | 19303 |
| 15 and 172 | 2580 |
| 33 and 192 | 2112 |