Least Common Multiple (LCM) of 52 and 195
The least common multiple (LCM) of 52 and 195 is 780.
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 52 and 195?
First, calculate the GCD of 52 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 195 = 0 remainder 52 |
| 2 | 195 ÷ 52 = 3 remainder 39 |
| 3 | 52 ÷ 39 = 1 remainder 13 |
| 4 | 39 ÷ 13 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 107 | 107 |
| 12 and 176 | 528 |
| 103 and 120 | 12360 |
| 117 and 89 | 10413 |
| 136 and 192 | 3264 |