Least Common Multiple (LCM) of 119 and 145
The least common multiple (LCM) of 119 and 145 is 17255.
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 145?
First, calculate the GCD of 119 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 145 = 0 remainder 119 |
| 2 | 145 ÷ 119 = 1 remainder 26 |
| 3 | 119 ÷ 26 = 4 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 162 | 1296 |
| 24 and 19 | 456 |
| 15 and 131 | 1965 |
| 170 and 54 | 4590 |
| 75 and 184 | 13800 |