Least Common Multiple (LCM) of 170 and 144
The least common multiple (LCM) of 170 and 144 is 12240.
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 144?
First, calculate the GCD of 170 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 144 = 1 remainder 26 |
| 2 | 144 ÷ 26 = 5 remainder 14 |
| 3 | 26 ÷ 14 = 1 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 43 | 4816 |
| 191 and 167 | 31897 |
| 122 and 190 | 11590 |
| 194 and 82 | 7954 |
| 162 and 164 | 13284 |