Least Common Multiple (LCM) of 30 and 177
The least common multiple (LCM) of 30 and 177 is 1770.
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 177?
First, calculate the GCD of 30 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 177 = 0 remainder 30 |
| 2 | 177 ÷ 30 = 5 remainder 27 |
| 3 | 30 ÷ 27 = 1 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 131 | 13231 |
| 13 and 64 | 832 |
| 111 and 50 | 5550 |
| 186 and 185 | 34410 |
| 146 and 54 | 3942 |