Least Common Multiple (LCM) of 105 and 160
The least common multiple (LCM) of 105 and 160 is 3360.
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 105 and 160?
First, calculate the GCD of 105 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 160 = 0 remainder 105 |
| 2 | 160 ÷ 105 = 1 remainder 55 |
| 3 | 105 ÷ 55 = 1 remainder 50 |
| 4 | 55 ÷ 50 = 1 remainder 5 |
| 5 | 50 ÷ 5 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 187 | 748 |
| 120 and 200 | 600 |
| 78 and 168 | 2184 |
| 12 and 124 | 372 |
| 102 and 109 | 11118 |