Least Common Multiple (LCM) of 160 and 111
The least common multiple (LCM) of 160 and 111 is 17760.
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 111?
First, calculate the GCD of 160 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 111 = 1 remainder 49 |
| 2 | 111 ÷ 49 = 2 remainder 13 |
| 3 | 49 ÷ 13 = 3 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 45 | 8460 |
| 48 and 65 | 3120 |
| 89 and 161 | 14329 |
| 78 and 198 | 2574 |
| 137 and 52 | 7124 |