Least Common Multiple (LCM) of 175 and 102
The least common multiple (LCM) of 175 and 102 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 175 and 102?
First, calculate the GCD of 175 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 102 = 1 remainder 73 |
| 2 | 102 ÷ 73 = 1 remainder 29 |
| 3 | 73 ÷ 29 = 2 remainder 15 |
| 4 | 29 ÷ 15 = 1 remainder 14 |
| 5 | 15 ÷ 14 = 1 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 118 | 10620 |
| 37 and 130 | 4810 |
| 172 and 82 | 7052 |
| 78 and 21 | 546 |
| 186 and 97 | 18042 |