Least Common Multiple (LCM) of 144 and 109
The least common multiple (LCM) of 144 and 109 is 15696.
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 109?
First, calculate the GCD of 144 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 109 = 1 remainder 35 |
| 2 | 109 ÷ 35 = 3 remainder 4 |
| 3 | 35 ÷ 4 = 8 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 192 | 3648 |
| 76 and 57 | 228 |
| 75 and 181 | 13575 |
| 14 and 42 | 42 |
| 119 and 116 | 13804 |