Least Common Multiple (LCM) of 145 and 104
The least common multiple (LCM) of 145 and 104 is 15080.
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 104?
First, calculate the GCD of 145 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 104 = 1 remainder 41 |
| 2 | 104 ÷ 41 = 2 remainder 22 |
| 3 | 41 ÷ 22 = 1 remainder 19 |
| 4 | 22 ÷ 19 = 1 remainder 3 |
| 5 | 19 ÷ 3 = 6 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 120 | 360 |
| 79 and 152 | 12008 |
| 76 and 129 | 9804 |
| 22 and 186 | 2046 |
| 174 and 107 | 18618 |