Least Common Multiple (LCM) of 30 and 176
The least common multiple (LCM) of 30 and 176 is 2640.
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 176?
First, calculate the GCD of 30 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 176 = 0 remainder 30 |
| 2 | 176 ÷ 30 = 5 remainder 26 |
| 3 | 30 ÷ 26 = 1 remainder 4 |
| 4 | 26 ÷ 4 = 6 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 59 | 9086 |
| 156 and 159 | 8268 |
| 153 and 52 | 7956 |
| 142 and 148 | 10508 |
| 173 and 143 | 24739 |