Least Common Multiple (LCM) of 85 and 142
The least common multiple (LCM) of 85 and 142 is 12070.
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 142?
First, calculate the GCD of 85 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 142 = 0 remainder 85 |
| 2 | 142 ÷ 85 = 1 remainder 57 |
| 3 | 85 ÷ 57 = 1 remainder 28 |
| 4 | 57 ÷ 28 = 2 remainder 1 |
| 5 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 29 | 4553 |
| 65 and 49 | 3185 |
| 10 and 179 | 1790 |
| 30 and 168 | 840 |
| 52 and 178 | 4628 |