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 |
|---|---|
| 107 and 122 | 13054 |
| 103 and 153 | 15759 |
| 168 and 194 | 16296 |
| 130 and 136 | 8840 |
| 81 and 94 | 7614 |