Least Common Multiple (LCM) of 75 and 92
The least common multiple (LCM) of 75 and 92 is 6900.
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 92?
First, calculate the GCD of 75 and 92 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 92 = 0 remainder 75 |
| 2 | 92 ÷ 75 = 1 remainder 17 |
| 3 | 75 ÷ 17 = 4 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 147 | 1470 |
| 160 and 177 | 28320 |
| 33 and 166 | 5478 |
| 72 and 153 | 1224 |
| 55 and 152 | 8360 |