Least Common Multiple (LCM) of 70 and 185
The least common multiple (LCM) of 70 and 185 is 2590.
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 70 and 185?
First, calculate the GCD of 70 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 185 = 0 remainder 70 |
| 2 | 185 ÷ 70 = 2 remainder 45 |
| 3 | 70 ÷ 45 = 1 remainder 25 |
| 4 | 45 ÷ 25 = 1 remainder 20 |
| 5 | 25 ÷ 20 = 1 remainder 5 |
| 6 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 103 | 2266 |
| 22 and 55 | 110 |
| 140 and 133 | 2660 |
| 165 and 160 | 5280 |
| 47 and 84 | 3948 |