Least Common Multiple (LCM) of 101 and 145
The least common multiple (LCM) of 101 and 145 is 14645.
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 101 and 145?
First, calculate the GCD of 101 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 145 = 0 remainder 101 |
| 2 | 145 ÷ 101 = 1 remainder 44 |
| 3 | 101 ÷ 44 = 2 remainder 13 |
| 4 | 44 ÷ 13 = 3 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 50 | 8950 |
| 200 and 105 | 4200 |
| 85 and 35 | 595 |
| 62 and 51 | 3162 |
| 49 and 144 | 7056 |