Least Common Multiple (LCM) of 20 and 112
The least common multiple (LCM) of 20 and 112 is 560.
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 20 and 112?
First, calculate the GCD of 20 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 112 = 0 remainder 20 |
| 2 | 112 ÷ 20 = 5 remainder 12 |
| 3 | 20 ÷ 12 = 1 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 32 | 2528 |
| 19 and 87 | 1653 |
| 145 and 58 | 290 |
| 19 and 81 | 1539 |
| 107 and 190 | 20330 |