Least Common Multiple (LCM) of 85 and 160
The least common multiple (LCM) of 85 and 160 is 2720.
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 85 and 160?
First, calculate the GCD of 85 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 160 = 0 remainder 85 |
| 2 | 160 ÷ 85 = 1 remainder 75 |
| 3 | 85 ÷ 75 = 1 remainder 10 |
| 4 | 75 ÷ 10 = 7 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 185 | 8880 |
| 35 and 168 | 840 |
| 12 and 145 | 1740 |
| 102 and 65 | 6630 |
| 76 and 108 | 2052 |