Least Common Multiple (LCM) of 144 and 119
The least common multiple (LCM) of 144 and 119 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 144 and 119?
First, calculate the GCD of 144 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 119 = 1 remainder 25 |
| 2 | 119 ÷ 25 = 4 remainder 19 |
| 3 | 25 ÷ 19 = 1 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 98 | 3038 |
| 117 and 66 | 2574 |
| 28 and 26 | 364 |
| 141 and 191 | 26931 |
| 150 and 120 | 600 |