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 |
|---|---|
| 39 and 50 | 1950 |
| 67 and 106 | 7102 |
| 77 and 142 | 10934 |
| 101 and 173 | 17473 |
| 43 and 30 | 1290 |