Least Common Multiple (LCM) of 144 and 105
The least common multiple (LCM) of 144 and 105 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 144 and 105?
First, calculate the GCD of 144 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 105 = 1 remainder 39 |
| 2 | 105 ÷ 39 = 2 remainder 27 |
| 3 | 39 ÷ 27 = 1 remainder 12 |
| 4 | 27 ÷ 12 = 2 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 121 | 4114 |
| 170 and 85 | 170 |
| 96 and 81 | 2592 |
| 77 and 40 | 3080 |
| 150 and 120 | 600 |