Least Common Multiple (LCM) of 160 and 198
The least common multiple (LCM) of 160 and 198 is 15840.
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 198?
First, calculate the GCD of 160 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 198 = 0 remainder 160 |
| 2 | 198 ÷ 160 = 1 remainder 38 |
| 3 | 160 ÷ 38 = 4 remainder 8 |
| 4 | 38 ÷ 8 = 4 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 32 | 4640 |
| 69 and 123 | 2829 |
| 20 and 30 | 60 |
| 138 and 199 | 27462 |
| 46 and 114 | 2622 |