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 |
|---|---|
| 171 and 100 | 17100 |
| 61 and 79 | 4819 |
| 178 and 28 | 2492 |
| 150 and 136 | 10200 |
| 28 and 21 | 84 |