Least Common Multiple (LCM) of 45 and 56
The least common multiple (LCM) of 45 and 56 is 2520.
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 45 and 56?
First, calculate the GCD of 45 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 56 = 0 remainder 45 |
| 2 | 56 ÷ 45 = 1 remainder 11 |
| 3 | 45 ÷ 11 = 4 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 13 | 1729 |
| 24 and 111 | 888 |
| 80 and 65 | 1040 |
| 10 and 81 | 810 |
| 61 and 62 | 3782 |