Least Common Multiple (LCM) of 52 and 102
The least common multiple (LCM) of 52 and 102 is 2652.
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 52 and 102?
First, calculate the GCD of 52 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 102 = 0 remainder 52 |
| 2 | 102 ÷ 52 = 1 remainder 50 |
| 3 | 52 ÷ 50 = 1 remainder 2 |
| 4 | 50 ÷ 2 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 52 | 260 |
| 90 and 100 | 900 |
| 64 and 98 | 3136 |
| 152 and 117 | 17784 |
| 116 and 198 | 11484 |