Least Common Multiple (LCM) of 35 and 171
The least common multiple (LCM) of 35 and 171 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 35 and 171?
First, calculate the GCD of 35 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 171 = 0 remainder 35 |
| 2 | 171 ÷ 35 = 4 remainder 31 |
| 3 | 35 ÷ 31 = 1 remainder 4 |
| 4 | 31 ÷ 4 = 7 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 68 | 1020 |
| 40 and 35 | 280 |
| 59 and 136 | 8024 |
| 146 and 48 | 3504 |
| 189 and 176 | 33264 |