Least Common Multiple (LCM) of 145 and 119
The least common multiple (LCM) of 145 and 119 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 145 and 119?
First, calculate the GCD of 145 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 119 = 1 remainder 26 |
| 2 | 119 ÷ 26 = 4 remainder 15 |
| 3 | 26 ÷ 15 = 1 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 120 | 10680 |
| 11 and 31 | 341 |
| 147 and 42 | 294 |
| 128 and 137 | 17536 |
| 140 and 195 | 5460 |