Least Common Multiple (LCM) of 77 and 170
The least common multiple (LCM) of 77 and 170 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 77 and 170?
First, calculate the GCD of 77 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 170 = 0 remainder 77 |
| 2 | 170 ÷ 77 = 2 remainder 16 |
| 3 | 77 ÷ 16 = 4 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 52 | 3900 |
| 25 and 153 | 3825 |
| 72 and 179 | 12888 |
| 120 and 59 | 7080 |
| 104 and 182 | 728 |