Least Common Multiple (LCM) of 195 and 53
The least common multiple (LCM) of 195 and 53 is 10335.
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 53?
First, calculate the GCD of 195 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 53 = 3 remainder 36 |
| 2 | 53 ÷ 36 = 1 remainder 17 |
| 3 | 36 ÷ 17 = 2 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 31 | 620 |
| 119 and 196 | 3332 |
| 123 and 138 | 5658 |
| 168 and 113 | 18984 |
| 62 and 49 | 3038 |