Least Common Multiple (LCM) of 119 and 144
The least common multiple (LCM) of 119 and 144 is 17136.
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 119 and 144?
First, calculate the GCD of 119 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 144 = 0 remainder 119 |
| 2 | 144 ÷ 119 = 1 remainder 25 |
| 3 | 119 ÷ 25 = 4 remainder 19 |
| 4 | 25 ÷ 19 = 1 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 200 | 12200 |
| 128 and 67 | 8576 |
| 136 and 109 | 14824 |
| 146 and 35 | 5110 |
| 186 and 116 | 10788 |