Least Common Multiple (LCM) of 109 and 150
The least common multiple (LCM) of 109 and 150 is 16350.
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 109 and 150?
First, calculate the GCD of 109 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 150 = 0 remainder 109 |
| 2 | 150 ÷ 109 = 1 remainder 41 |
| 3 | 109 ÷ 41 = 2 remainder 27 |
| 4 | 41 ÷ 27 = 1 remainder 14 |
| 5 | 27 ÷ 14 = 1 remainder 13 |
| 6 | 14 ÷ 13 = 1 remainder 1 |
| 7 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 120 | 3000 |
| 63 and 34 | 2142 |
| 99 and 66 | 198 |
| 186 and 159 | 9858 |
| 73 and 200 | 14600 |