Least Common Multiple (LCM) of 160 and 67
The least common multiple (LCM) of 160 and 67 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 160 and 67?
First, calculate the GCD of 160 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 67 = 2 remainder 26 |
| 2 | 67 ÷ 26 = 2 remainder 15 |
| 3 | 26 ÷ 15 = 1 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 85 | 1360 |
| 195 and 156 | 780 |
| 121 and 167 | 20207 |
| 66 and 79 | 5214 |
| 116 and 63 | 7308 |