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 |
|---|---|
| 196 and 153 | 29988 |
| 192 and 182 | 17472 |
| 116 and 109 | 12644 |
| 119 and 45 | 5355 |
| 31 and 174 | 5394 |