Least Common Multiple (LCM) of 170 and 67
The least common multiple (LCM) of 170 and 67 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 170 and 67?
First, calculate the GCD of 170 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 67 = 2 remainder 36 |
| 2 | 67 ÷ 36 = 1 remainder 31 |
| 3 | 36 ÷ 31 = 1 remainder 5 |
| 4 | 31 ÷ 5 = 6 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 17 | 2737 |
| 112 and 37 | 4144 |
| 193 and 63 | 12159 |
| 112 and 157 | 17584 |
| 167 and 134 | 22378 |