Least Common Multiple (LCM) of 116 and 150
The least common multiple (LCM) of 116 and 150 is 8700.
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 116 and 150?
First, calculate the GCD of 116 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 150 = 0 remainder 116 |
| 2 | 150 ÷ 116 = 1 remainder 34 |
| 3 | 116 ÷ 34 = 3 remainder 14 |
| 4 | 34 ÷ 14 = 2 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 74 | 814 |
| 136 and 19 | 2584 |
| 140 and 143 | 20020 |
| 137 and 75 | 10275 |
| 168 and 128 | 2688 |