Least Common Multiple (LCM) of 71 and 170
The least common multiple (LCM) of 71 and 170 is 12070.
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 71 and 170?
First, calculate the GCD of 71 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 170 = 0 remainder 71 |
| 2 | 170 ÷ 71 = 2 remainder 28 |
| 3 | 71 ÷ 28 = 2 remainder 15 |
| 4 | 28 ÷ 15 = 1 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 55 | 110 |
| 195 and 70 | 2730 |
| 146 and 21 | 3066 |
| 42 and 21 | 42 |
| 103 and 99 | 10197 |