Least Common Multiple (LCM) of 13 and 52
The least common multiple (LCM) of 13 and 52 is 52.
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 13 and 52?
First, calculate the GCD of 13 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 52 = 0 remainder 13 |
| 2 | 52 ÷ 13 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 189 | 1890 |
| 114 and 71 | 8094 |
| 105 and 75 | 525 |
| 155 and 154 | 23870 |
| 138 and 32 | 2208 |