Least Common Multiple (LCM) of 160 and 189
The least common multiple (LCM) of 160 and 189 is 30240.
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 189?
First, calculate the GCD of 160 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 189 = 0 remainder 160 |
| 2 | 189 ÷ 160 = 1 remainder 29 |
| 3 | 160 ÷ 29 = 5 remainder 15 |
| 4 | 29 ÷ 15 = 1 remainder 14 |
| 5 | 15 ÷ 14 = 1 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 99 | 1287 |
| 141 and 82 | 11562 |
| 185 and 113 | 20905 |
| 25 and 200 | 200 |
| 56 and 121 | 6776 |