Least Common Multiple (LCM) of 177 and 144
The least common multiple (LCM) of 177 and 144 is 8496.
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 144?
First, calculate the GCD of 177 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 144 = 1 remainder 33 |
| 2 | 144 ÷ 33 = 4 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 176 | 6512 |
| 109 and 100 | 10900 |
| 133 and 113 | 15029 |
| 124 and 105 | 13020 |
| 118 and 111 | 13098 |