Least Common Multiple (LCM) of 56 and 111
The least common multiple (LCM) of 56 and 111 is 6216.
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 111?
First, calculate the GCD of 56 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 111 = 0 remainder 56 |
| 2 | 111 ÷ 56 = 1 remainder 55 |
| 3 | 56 ÷ 55 = 1 remainder 1 |
| 4 | 55 ÷ 1 = 55 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 85 | 7565 |
| 196 and 160 | 7840 |
| 180 and 111 | 6660 |
| 13 and 163 | 2119 |
| 144 and 200 | 3600 |