Least Common Multiple (LCM) of 144 and 170
The least common multiple (LCM) of 144 and 170 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 144 and 170?
First, calculate the GCD of 144 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 170 = 0 remainder 144 |
| 2 | 170 ÷ 144 = 1 remainder 26 |
| 3 | 144 ÷ 26 = 5 remainder 14 |
| 4 | 26 ÷ 14 = 1 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 20 | 1180 |
| 117 and 126 | 1638 |
| 106 and 115 | 12190 |
| 59 and 199 | 11741 |
| 107 and 13 | 1391 |