Least Common Multiple (LCM) of 177 and 74
The least common multiple (LCM) of 177 and 74 is 13098.
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 74?
First, calculate the GCD of 177 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 74 = 2 remainder 29 |
| 2 | 74 ÷ 29 = 2 remainder 16 |
| 3 | 29 ÷ 16 = 1 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 182 | 1092 |
| 168 and 99 | 5544 |
| 164 and 117 | 19188 |
| 28 and 12 | 84 |
| 166 and 114 | 9462 |