Least Common Multiple (LCM) of 144 and 67
The least common multiple (LCM) of 144 and 67 is 9648.
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 67?
First, calculate the GCD of 144 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 67 = 2 remainder 10 |
| 2 | 67 ÷ 10 = 6 remainder 7 |
| 3 | 10 ÷ 7 = 1 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 181 | 19729 |
| 171 and 168 | 9576 |
| 108 and 190 | 10260 |
| 65 and 144 | 9360 |
| 196 and 33 | 6468 |