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 |
|---|---|
| 108 and 133 | 14364 |
| 74 and 132 | 4884 |
| 65 and 131 | 8515 |
| 114 and 10 | 570 |
| 35 and 187 | 6545 |