Least Common Multiple (LCM) of 75 and 176
The least common multiple (LCM) of 75 and 176 is 13200.
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 176?
First, calculate the GCD of 75 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 176 = 0 remainder 75 |
| 2 | 176 ÷ 75 = 2 remainder 26 |
| 3 | 75 ÷ 26 = 2 remainder 23 |
| 4 | 26 ÷ 23 = 1 remainder 3 |
| 5 | 23 ÷ 3 = 7 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 58 | 1566 |
| 61 and 190 | 11590 |
| 147 and 169 | 24843 |
| 159 and 85 | 13515 |
| 75 and 51 | 1275 |