Least Common Multiple (LCM) of 67 and 144
The least common multiple (LCM) of 67 and 144 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 67 and 144?
First, calculate the GCD of 67 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 144 = 0 remainder 67 |
| 2 | 144 ÷ 67 = 2 remainder 10 |
| 3 | 67 ÷ 10 = 6 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 96 | 9120 |
| 115 and 163 | 18745 |
| 144 and 113 | 16272 |
| 113 and 70 | 7910 |
| 143 and 39 | 429 |