Least Common Multiple (LCM) of 85 and 178
The least common multiple (LCM) of 85 and 178 is 15130.
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 178?
First, calculate the GCD of 85 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 178 = 0 remainder 85 |
| 2 | 178 ÷ 85 = 2 remainder 8 |
| 3 | 85 ÷ 8 = 10 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 152 | 27512 |
| 63 and 55 | 3465 |
| 154 and 154 | 154 |
| 83 and 192 | 15936 |
| 183 and 118 | 21594 |