Least Common Multiple (LCM) of 53 and 13
The least common multiple (LCM) of 53 and 13 is 689.
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 13?
First, calculate the GCD of 53 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 13 = 4 remainder 1 |
| 2 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 180 | 6660 |
| 52 and 141 | 7332 |
| 118 and 67 | 7906 |
| 195 and 126 | 8190 |
| 158 and 192 | 15168 |