Least Common Multiple (LCM) of 75 and 178
The least common multiple (LCM) of 75 and 178 is 13350.
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 178?
First, calculate the GCD of 75 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 178 = 0 remainder 75 |
| 2 | 178 ÷ 75 = 2 remainder 28 |
| 3 | 75 ÷ 28 = 2 remainder 19 |
| 4 | 28 ÷ 19 = 1 remainder 9 |
| 5 | 19 ÷ 9 = 2 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 165 | 1155 |
| 111 and 183 | 6771 |
| 52 and 163 | 8476 |
| 197 and 96 | 18912 |
| 164 and 64 | 2624 |