Least Common Multiple (LCM) of 170 and 77
The least common multiple (LCM) of 170 and 77 is 13090.
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 170 and 77?
First, calculate the GCD of 170 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 77 = 2 remainder 16 |
| 2 | 77 ÷ 16 = 4 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 73 | 7300 |
| 17 and 143 | 2431 |
| 105 and 20 | 420 |
| 97 and 190 | 18430 |
| 27 and 155 | 4185 |