Least Common Multiple (LCM) of 67 and 160
The least common multiple (LCM) of 67 and 160 is 10720.
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 67 and 160?
First, calculate the GCD of 67 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 160 = 0 remainder 67 |
| 2 | 160 ÷ 67 = 2 remainder 26 |
| 3 | 67 ÷ 26 = 2 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 39 | 741 |
| 55 and 163 | 8965 |
| 196 and 120 | 5880 |
| 24 and 36 | 72 |
| 174 and 53 | 9222 |