Least Common Multiple (LCM) of 102 and 175
The least common multiple (LCM) of 102 and 175 is 17850.
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 102 and 175?
First, calculate the GCD of 102 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 175 = 0 remainder 102 |
| 2 | 175 ÷ 102 = 1 remainder 73 |
| 3 | 102 ÷ 73 = 1 remainder 29 |
| 4 | 73 ÷ 29 = 2 remainder 15 |
| 5 | 29 ÷ 15 = 1 remainder 14 |
| 6 | 15 ÷ 14 = 1 remainder 1 |
| 7 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 117 | 13455 |
| 198 and 133 | 26334 |
| 112 and 18 | 1008 |
| 55 and 115 | 1265 |
| 70 and 79 | 5530 |