Least Common Multiple (LCM) of 105 and 144
The least common multiple (LCM) of 105 and 144 is 5040.
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 105 and 144?
First, calculate the GCD of 105 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 144 = 0 remainder 105 |
| 2 | 144 ÷ 105 = 1 remainder 39 |
| 3 | 105 ÷ 39 = 2 remainder 27 |
| 4 | 39 ÷ 27 = 1 remainder 12 |
| 5 | 27 ÷ 12 = 2 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 153 | 8109 |
| 68 and 159 | 10812 |
| 112 and 47 | 5264 |
| 170 and 122 | 10370 |
| 80 and 166 | 6640 |