Least Common Multiple (LCM) of 195 and 76
The least common multiple (LCM) of 195 and 76 is 14820.
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 76?
First, calculate the GCD of 195 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 76 = 2 remainder 43 |
| 2 | 76 ÷ 43 = 1 remainder 33 |
| 3 | 43 ÷ 33 = 1 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 89 | 10146 |
| 49 and 111 | 5439 |
| 130 and 59 | 7670 |
| 70 and 44 | 1540 |
| 67 and 46 | 3082 |