Least Common Multiple (LCM) of 103 and 150
The least common multiple (LCM) of 103 and 150 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 103 and 150?
First, calculate the GCD of 103 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 150 = 0 remainder 103 |
| 2 | 150 ÷ 103 = 1 remainder 47 |
| 3 | 103 ÷ 47 = 2 remainder 9 |
| 4 | 47 ÷ 9 = 5 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 13 | 1794 |
| 14 and 88 | 616 |
| 74 and 185 | 370 |
| 89 and 29 | 2581 |
| 146 and 135 | 19710 |