Least Common Multiple (LCM) of 171 and 75
The least common multiple (LCM) of 171 and 75 is 4275.
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 171 and 75?
First, calculate the GCD of 171 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 75 = 2 remainder 21 |
| 2 | 75 ÷ 21 = 3 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 16 | 1424 |
| 24 and 80 | 240 |
| 70 and 71 | 4970 |
| 62 and 35 | 2170 |
| 140 and 172 | 6020 |