Least Common Multiple (LCM) of 195 and 88
The least common multiple (LCM) of 195 and 88 is 17160.
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 195 and 88?
First, calculate the GCD of 195 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 88 = 2 remainder 19 |
| 2 | 88 ÷ 19 = 4 remainder 12 |
| 3 | 19 ÷ 12 = 1 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 60 | 780 |
| 24 and 124 | 744 |
| 144 and 39 | 1872 |
| 110 and 105 | 2310 |
| 72 and 27 | 216 |