Least Common Multiple (LCM) of 99 and 172
The least common multiple (LCM) of 99 and 172 is 17028.
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 172?
First, calculate the GCD of 99 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 172 = 0 remainder 99 |
| 2 | 172 ÷ 99 = 1 remainder 73 |
| 3 | 99 ÷ 73 = 1 remainder 26 |
| 4 | 73 ÷ 26 = 2 remainder 21 |
| 5 | 26 ÷ 21 = 1 remainder 5 |
| 6 | 21 ÷ 5 = 4 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 95 | 2945 |
| 145 and 103 | 14935 |
| 135 and 149 | 20115 |
| 117 and 103 | 12051 |
| 65 and 87 | 5655 |