Least Common Multiple (LCM) of 99 and 173
The least common multiple (LCM) of 99 and 173 is 17127.
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 99 and 173?
First, calculate the GCD of 99 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 173 = 0 remainder 99 |
| 2 | 173 ÷ 99 = 1 remainder 74 |
| 3 | 99 ÷ 74 = 1 remainder 25 |
| 4 | 74 ÷ 25 = 2 remainder 24 |
| 5 | 25 ÷ 24 = 1 remainder 1 |
| 6 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 36 | 2556 |
| 165 and 196 | 32340 |
| 116 and 144 | 4176 |
| 18 and 61 | 1098 |
| 164 and 67 | 10988 |