Least Common Multiple (LCM) of 46 and 177
The least common multiple (LCM) of 46 and 177 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 46 and 177?
First, calculate the GCD of 46 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 177 = 0 remainder 46 |
| 2 | 177 ÷ 46 = 3 remainder 39 |
| 3 | 46 ÷ 39 = 1 remainder 7 |
| 4 | 39 ÷ 7 = 5 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 111 | 5439 |
| 177 and 122 | 21594 |
| 67 and 123 | 8241 |
| 82 and 108 | 4428 |
| 90 and 153 | 1530 |