Least Common Multiple (LCM) of 160 and 193
The least common multiple (LCM) of 160 and 193 is 30880.
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 160 and 193?
First, calculate the GCD of 160 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 193 = 0 remainder 160 |
| 2 | 193 ÷ 160 = 1 remainder 33 |
| 3 | 160 ÷ 33 = 4 remainder 28 |
| 4 | 33 ÷ 28 = 1 remainder 5 |
| 5 | 28 ÷ 5 = 5 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 71 | 2414 |
| 30 and 27 | 270 |
| 193 and 88 | 16984 |
| 39 and 178 | 6942 |
| 40 and 109 | 4360 |