Least Common Multiple (LCM) of 19 and 160
The least common multiple (LCM) of 19 and 160 is 3040.
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 19 and 160?
First, calculate the GCD of 19 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 160 = 0 remainder 19 |
| 2 | 160 ÷ 19 = 8 remainder 8 |
| 3 | 19 ÷ 8 = 2 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 40 | 2840 |
| 135 and 84 | 3780 |
| 124 and 49 | 6076 |
| 126 and 188 | 11844 |
| 105 and 31 | 3255 |