Least Common Multiple (LCM) of 102 and 49
The least common multiple (LCM) of 102 and 49 is 4998.
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 49?
First, calculate the GCD of 102 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 49 = 2 remainder 4 |
| 2 | 49 ÷ 4 = 12 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 171 | 23427 |
| 99 and 132 | 396 |
| 187 and 114 | 21318 |
| 78 and 68 | 2652 |
| 10 and 99 | 990 |