Least Common Multiple (LCM) of 67 and 170
The least common multiple (LCM) of 67 and 170 is 11390.
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 67 and 170?
First, calculate the GCD of 67 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 170 = 0 remainder 67 |
| 2 | 170 ÷ 67 = 2 remainder 36 |
| 3 | 67 ÷ 36 = 1 remainder 31 |
| 4 | 36 ÷ 31 = 1 remainder 5 |
| 5 | 31 ÷ 5 = 6 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 89 | 2492 |
| 81 and 142 | 11502 |
| 51 and 171 | 2907 |
| 56 and 107 | 5992 |
| 158 and 97 | 15326 |