Least Common Multiple (LCM) of 177 and 67
The least common multiple (LCM) of 177 and 67 is 11859.
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 67?
First, calculate the GCD of 177 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 67 = 2 remainder 43 |
| 2 | 67 ÷ 43 = 1 remainder 24 |
| 3 | 43 ÷ 24 = 1 remainder 19 |
| 4 | 24 ÷ 19 = 1 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 101 | 11110 |
| 67 and 72 | 4824 |
| 178 and 74 | 6586 |
| 39 and 17 | 663 |
| 112 and 61 | 6832 |