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 |
|---|---|
| 74 and 20 | 740 |
| 34 and 192 | 3264 |
| 56 and 164 | 2296 |
| 124 and 31 | 124 |
| 111 and 81 | 2997 |