Least Common Multiple (LCM) of 114 and 150
The least common multiple (LCM) of 114 and 150 is 2850.
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 114 and 150?
First, calculate the GCD of 114 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 150 = 0 remainder 114 |
| 2 | 150 ÷ 114 = 1 remainder 36 |
| 3 | 114 ÷ 36 = 3 remainder 6 |
| 4 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 42 | 546 |
| 85 and 37 | 3145 |
| 24 and 133 | 3192 |
| 112 and 15 | 1680 |
| 12 and 131 | 1572 |