Least Common Multiple (LCM) of 53 and 68
The least common multiple (LCM) of 53 and 68 is 3604.
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 68?
First, calculate the GCD of 53 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 68 = 0 remainder 53 |
| 2 | 68 ÷ 53 = 1 remainder 15 |
| 3 | 53 ÷ 15 = 3 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 194 | 3880 |
| 117 and 174 | 6786 |
| 42 and 199 | 8358 |
| 158 and 173 | 27334 |
| 189 and 13 | 2457 |