Least Common Multiple (LCM) of 160 and 195
The least common multiple (LCM) of 160 and 195 is 6240.
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 195?
First, calculate the GCD of 160 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 195 = 0 remainder 160 |
| 2 | 195 ÷ 160 = 1 remainder 35 |
| 3 | 160 ÷ 35 = 4 remainder 20 |
| 4 | 35 ÷ 20 = 1 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 175 | 13650 |
| 47 and 107 | 5029 |
| 60 and 107 | 6420 |
| 172 and 141 | 24252 |
| 56 and 32 | 224 |