Least Common Multiple (LCM) of 145 and 177
The least common multiple (LCM) of 145 and 177 is 25665.
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 145 and 177?
First, calculate the GCD of 145 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 177 = 0 remainder 145 |
| 2 | 177 ÷ 145 = 1 remainder 32 |
| 3 | 145 ÷ 32 = 4 remainder 17 |
| 4 | 32 ÷ 17 = 1 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 88 | 1672 |
| 196 and 120 | 5880 |
| 45 and 12 | 180 |
| 99 and 170 | 16830 |
| 38 and 137 | 5206 |