Least Common Multiple (LCM) of 171 and 35
The least common multiple (LCM) of 171 and 35 is 5985.
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 35?
First, calculate the GCD of 171 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 35 = 4 remainder 31 |
| 2 | 35 ÷ 31 = 1 remainder 4 |
| 3 | 31 ÷ 4 = 7 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 140 | 140 |
| 193 and 109 | 21037 |
| 105 and 57 | 1995 |
| 73 and 104 | 7592 |
| 46 and 157 | 7222 |