Least Common Multiple (LCM) of 120 and 85
The least common multiple (LCM) of 120 and 85 is 2040.
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 120 and 85?
First, calculate the GCD of 120 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 85 = 1 remainder 35 |
| 2 | 85 ÷ 35 = 2 remainder 15 |
| 3 | 35 ÷ 15 = 2 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 177 | 30975 |
| 164 and 178 | 14596 |
| 104 and 104 | 104 |
| 17 and 153 | 153 |
| 99 and 14 | 1386 |