Least Common Multiple (LCM) of 14 and 52
The least common multiple (LCM) of 14 and 52 is 364.
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 14 and 52?
First, calculate the GCD of 14 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 52 = 0 remainder 14 |
| 2 | 52 ÷ 14 = 3 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 67 | 1273 |
| 51 and 99 | 1683 |
| 161 and 95 | 15295 |
| 182 and 76 | 6916 |
| 116 and 47 | 5452 |