Least Common Multiple (LCM) of 53 and 102
The least common multiple (LCM) of 53 and 102 is 5406.
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 102?
First, calculate the GCD of 53 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 102 = 0 remainder 53 |
| 2 | 102 ÷ 53 = 1 remainder 49 |
| 3 | 53 ÷ 49 = 1 remainder 4 |
| 4 | 49 ÷ 4 = 12 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 186 | 5952 |
| 187 and 131 | 24497 |
| 145 and 68 | 9860 |
| 199 and 117 | 23283 |
| 108 and 135 | 540 |