Least Common Multiple (LCM) of 114 and 75
The least common multiple (LCM) of 114 and 75 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 75?
First, calculate the GCD of 114 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 75 = 1 remainder 39 |
| 2 | 75 ÷ 39 = 1 remainder 36 |
| 3 | 39 ÷ 36 = 1 remainder 3 |
| 4 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 42 | 3570 |
| 199 and 74 | 14726 |
| 99 and 146 | 14454 |
| 103 and 143 | 14729 |
| 147 and 134 | 19698 |