Least Common Multiple (LCM) of 175 and 187
The least common multiple (LCM) of 175 and 187 is 32725.
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 187?
First, calculate the GCD of 175 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 187 = 0 remainder 175 |
| 2 | 187 ÷ 175 = 1 remainder 12 |
| 3 | 175 ÷ 12 = 14 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 90 | 1440 |
| 50 and 155 | 1550 |
| 40 and 196 | 1960 |
| 71 and 44 | 3124 |
| 81 and 198 | 1782 |