Least Common Multiple (LCM) of 135 and 176
The least common multiple (LCM) of 135 and 176 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 135 and 176?
First, calculate the GCD of 135 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 176 = 0 remainder 135 |
| 2 | 176 ÷ 135 = 1 remainder 41 |
| 3 | 135 ÷ 41 = 3 remainder 12 |
| 4 | 41 ÷ 12 = 3 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 120 | 4440 |
| 142 and 77 | 10934 |
| 54 and 162 | 162 |
| 69 and 197 | 13593 |
| 24 and 150 | 600 |