Least Common Multiple (LCM) of 150 and 103
The least common multiple (LCM) of 150 and 103 is 15450.
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 150 and 103?
First, calculate the GCD of 150 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 103 = 1 remainder 47 |
| 2 | 103 ÷ 47 = 2 remainder 9 |
| 3 | 47 ÷ 9 = 5 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 83 | 14608 |
| 159 and 191 | 30369 |
| 45 and 17 | 765 |
| 40 and 68 | 680 |
| 133 and 35 | 665 |