Least Common Multiple (LCM) of 178 and 75
The least common multiple (LCM) of 178 and 75 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 178 and 75?
First, calculate the GCD of 178 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 75 = 2 remainder 28 |
| 2 | 75 ÷ 28 = 2 remainder 19 |
| 3 | 28 ÷ 19 = 1 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 180 | 1260 |
| 101 and 88 | 8888 |
| 66 and 130 | 4290 |
| 106 and 43 | 4558 |
| 23 and 169 | 3887 |