Least Common Multiple (LCM) of 175 and 99
The least common multiple (LCM) of 175 and 99 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 175 and 99?
First, calculate the GCD of 175 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 99 = 1 remainder 76 |
| 2 | 99 ÷ 76 = 1 remainder 23 |
| 3 | 76 ÷ 23 = 3 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 46 | 1196 |
| 123 and 153 | 6273 |
| 126 and 10 | 630 |
| 103 and 46 | 4738 |
| 102 and 141 | 4794 |