Least Common Multiple (LCM) of 106 and 145
The least common multiple (LCM) of 106 and 145 is 15370.
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 106 and 145?
First, calculate the GCD of 106 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 145 = 0 remainder 106 |
| 2 | 145 ÷ 106 = 1 remainder 39 |
| 3 | 106 ÷ 39 = 2 remainder 28 |
| 4 | 39 ÷ 28 = 1 remainder 11 |
| 5 | 28 ÷ 11 = 2 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 75 | 1425 |
| 126 and 70 | 630 |
| 78 and 197 | 15366 |
| 94 and 75 | 7050 |
| 85 and 100 | 1700 |