Least Common Multiple (LCM) of 95 and 180
The least common multiple (LCM) of 95 and 180 is 3420.
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 95 and 180?
First, calculate the GCD of 95 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 95 ÷ 180 = 0 remainder 95 |
| 2 | 180 ÷ 95 = 1 remainder 85 |
| 3 | 95 ÷ 85 = 1 remainder 10 |
| 4 | 85 ÷ 10 = 8 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 100 | 400 |
| 30 and 67 | 2010 |
| 165 and 31 | 5115 |
| 102 and 75 | 2550 |
| 188 and 167 | 31396 |