Least Common Multiple (LCM) of 150 and 109
The least common multiple (LCM) of 150 and 109 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 150 and 109?
First, calculate the GCD of 150 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 109 = 1 remainder 41 |
| 2 | 109 ÷ 41 = 2 remainder 27 |
| 3 | 41 ÷ 27 = 1 remainder 14 |
| 4 | 27 ÷ 14 = 1 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 25 | 3150 |
| 138 and 64 | 4416 |
| 129 and 185 | 23865 |
| 21 and 67 | 1407 |
| 180 and 133 | 23940 |