Least Common Multiple (LCM) of 135 and 56
The least common multiple (LCM) of 135 and 56 is 7560.
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 56?
First, calculate the GCD of 135 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 56 = 2 remainder 23 |
| 2 | 56 ÷ 23 = 2 remainder 10 |
| 3 | 23 ÷ 10 = 2 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 165 | 5610 |
| 50 and 184 | 4600 |
| 196 and 181 | 35476 |
| 131 and 149 | 19519 |
| 75 and 170 | 2550 |