Least Common Multiple (LCM) of 176 and 135
The least common multiple (LCM) of 176 and 135 is 23760.
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 176 and 135?
First, calculate the GCD of 176 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 135 = 1 remainder 41 |
| 2 | 135 ÷ 41 = 3 remainder 12 |
| 3 | 41 ÷ 12 = 3 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 104 | 2600 |
| 172 and 186 | 15996 |
| 100 and 141 | 14100 |
| 11 and 199 | 2189 |
| 131 and 97 | 12707 |