Least Common Multiple (LCM) of 195 and 51
The least common multiple (LCM) of 195 and 51 is 3315.
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 51?
First, calculate the GCD of 195 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 51 = 3 remainder 42 |
| 2 | 51 ÷ 42 = 1 remainder 9 |
| 3 | 42 ÷ 9 = 4 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 192 | 12480 |
| 188 and 42 | 3948 |
| 150 and 107 | 16050 |
| 163 and 189 | 30807 |
| 129 and 13 | 1677 |