Least Common Multiple (LCM) of 109 and 160
The least common multiple (LCM) of 109 and 160 is 17440.
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 109 and 160?
First, calculate the GCD of 109 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 160 = 0 remainder 109 |
| 2 | 160 ÷ 109 = 1 remainder 51 |
| 3 | 109 ÷ 51 = 2 remainder 7 |
| 4 | 51 ÷ 7 = 7 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 43 | 4816 |
| 44 and 54 | 1188 |
| 16 and 101 | 1616 |
| 112 and 65 | 7280 |
| 48 and 110 | 2640 |