Least Common Multiple (LCM) of 102 and 53
The least common multiple (LCM) of 102 and 53 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 102 and 53?
First, calculate the GCD of 102 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 53 = 1 remainder 49 |
| 2 | 53 ÷ 49 = 1 remainder 4 |
| 3 | 49 ÷ 4 = 12 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 89 | 15486 |
| 166 and 176 | 14608 |
| 124 and 145 | 17980 |
| 96 and 25 | 2400 |
| 192 and 57 | 3648 |