Least Common Multiple (LCM) of 53 and 39
The least common multiple (LCM) of 53 and 39 is 2067.
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 53 and 39?
First, calculate the GCD of 53 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 39 = 1 remainder 14 |
| 2 | 39 ÷ 14 = 2 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 50 | 4950 |
| 143 and 136 | 19448 |
| 123 and 168 | 6888 |
| 78 and 113 | 8814 |
| 160 and 116 | 4640 |