Least Common Multiple (LCM) of 189 and 160
The least common multiple (LCM) of 189 and 160 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 189 and 160?
First, calculate the GCD of 189 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 160 = 1 remainder 29 |
| 2 | 160 ÷ 29 = 5 remainder 15 |
| 3 | 29 ÷ 15 = 1 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 74 | 1184 |
| 20 and 191 | 3820 |
| 189 and 158 | 29862 |
| 190 and 119 | 22610 |
| 76 and 144 | 2736 |