Least Common Multiple (LCM) of 74 and 177
The least common multiple (LCM) of 74 and 177 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 74 and 177?
First, calculate the GCD of 74 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 177 = 0 remainder 74 |
| 2 | 177 ÷ 74 = 2 remainder 29 |
| 3 | 74 ÷ 29 = 2 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 16 | 720 |
| 16 and 72 | 144 |
| 153 and 189 | 3213 |
| 98 and 171 | 16758 |
| 147 and 116 | 17052 |