Least Common Multiple (LCM) of 30 and 178
The least common multiple (LCM) of 30 and 178 is 2670.
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 30 and 178?
First, calculate the GCD of 30 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 178 = 0 remainder 30 |
| 2 | 178 ÷ 30 = 5 remainder 28 |
| 3 | 30 ÷ 28 = 1 remainder 2 |
| 4 | 28 ÷ 2 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 155 | 25730 |
| 77 and 26 | 2002 |
| 176 and 125 | 22000 |
| 177 and 83 | 14691 |
| 35 and 32 | 1120 |