Least Common Multiple (LCM) of 19 and 150
The least common multiple (LCM) of 19 and 150 is 2850.
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 19 and 150?
First, calculate the GCD of 19 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 150 = 0 remainder 19 |
| 2 | 150 ÷ 19 = 7 remainder 17 |
| 3 | 19 ÷ 17 = 1 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 52 | 5668 |
| 75 and 32 | 2400 |
| 81 and 20 | 1620 |
| 108 and 146 | 7884 |
| 198 and 52 | 5148 |