Least Common Multiple (LCM) of 160 and 197
The least common multiple (LCM) of 160 and 197 is 31520.
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 197?
First, calculate the GCD of 160 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 197 = 0 remainder 160 |
| 2 | 197 ÷ 160 = 1 remainder 37 |
| 3 | 160 ÷ 37 = 4 remainder 12 |
| 4 | 37 ÷ 12 = 3 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 75 | 5100 |
| 90 and 143 | 12870 |
| 10 and 78 | 390 |
| 42 and 54 | 378 |
| 163 and 19 | 3097 |