Least Common Multiple (LCM) of 85 and 140
The least common multiple (LCM) of 85 and 140 is 2380.
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 140?
First, calculate the GCD of 85 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 140 = 0 remainder 85 |
| 2 | 140 ÷ 85 = 1 remainder 55 |
| 3 | 85 ÷ 55 = 1 remainder 30 |
| 4 | 55 ÷ 30 = 1 remainder 25 |
| 5 | 30 ÷ 25 = 1 remainder 5 |
| 6 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 136 | 1768 |
| 69 and 146 | 10074 |
| 81 and 128 | 10368 |
| 114 and 43 | 4902 |
| 66 and 12 | 132 |