Least Common Multiple (LCM) of 99 and 175
The least common multiple (LCM) of 99 and 175 is 17325.
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 175?
First, calculate the GCD of 99 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 175 = 0 remainder 99 |
| 2 | 175 ÷ 99 = 1 remainder 76 |
| 3 | 99 ÷ 76 = 1 remainder 23 |
| 4 | 76 ÷ 23 = 3 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 81 | 14904 |
| 75 and 200 | 600 |
| 176 and 85 | 14960 |
| 21 and 129 | 903 |
| 164 and 103 | 16892 |