Least Common Multiple (LCM) of 88 and 195
The least common multiple (LCM) of 88 and 195 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 88 and 195?
First, calculate the GCD of 88 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 88 ÷ 195 = 0 remainder 88 |
| 2 | 195 ÷ 88 = 2 remainder 19 |
| 3 | 88 ÷ 19 = 4 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 100 | 3300 |
| 56 and 106 | 2968 |
| 14 and 173 | 2422 |
| 102 and 116 | 5916 |
| 139 and 66 | 9174 |