Least Common Multiple (LCM) of 75 and 112
The least common multiple (LCM) of 75 and 112 is 8400.
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 112?
First, calculate the GCD of 75 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 112 = 0 remainder 75 |
| 2 | 112 ÷ 75 = 1 remainder 37 |
| 3 | 75 ÷ 37 = 2 remainder 1 |
| 4 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 92 | 3956 |
| 128 and 159 | 20352 |
| 109 and 106 | 11554 |
| 68 and 200 | 3400 |
| 141 and 122 | 17202 |