Least Common Multiple (LCM) of 150 and 116
The least common multiple (LCM) of 150 and 116 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 150 and 116?
First, calculate the GCD of 150 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 116 = 1 remainder 34 |
| 2 | 116 ÷ 34 = 3 remainder 14 |
| 3 | 34 ÷ 14 = 2 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 105 | 10605 |
| 186 and 149 | 27714 |
| 195 and 115 | 4485 |
| 168 and 141 | 7896 |
| 17 and 111 | 1887 |