Least Common Multiple (LCM) of 177 and 46
The least common multiple (LCM) of 177 and 46 is 8142.
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 177 and 46?
First, calculate the GCD of 177 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 46 = 3 remainder 39 |
| 2 | 46 ÷ 39 = 1 remainder 7 |
| 3 | 39 ÷ 7 = 5 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 114 | 1938 |
| 179 and 136 | 24344 |
| 100 and 162 | 8100 |
| 71 and 143 | 10153 |
| 126 and 173 | 21798 |