Least Common Multiple (LCM) of 56 and 135
The least common multiple (LCM) of 56 and 135 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 56 and 135?
First, calculate the GCD of 56 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 135 = 0 remainder 56 |
| 2 | 135 ÷ 56 = 2 remainder 23 |
| 3 | 56 ÷ 23 = 2 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 23 | 3864 |
| 49 and 44 | 2156 |
| 195 and 124 | 24180 |
| 196 and 23 | 4508 |
| 123 and 42 | 1722 |