Least Common Multiple (LCM) of 75 and 114
The least common multiple (LCM) of 75 and 114 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 75 and 114?
First, calculate the GCD of 75 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 114 = 0 remainder 75 |
| 2 | 114 ÷ 75 = 1 remainder 39 |
| 3 | 75 ÷ 39 = 1 remainder 36 |
| 4 | 39 ÷ 36 = 1 remainder 3 |
| 5 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 100 | 7300 |
| 34 and 80 | 1360 |
| 68 and 136 | 136 |
| 45 and 69 | 1035 |
| 107 and 33 | 3531 |