Least Common Multiple (LCM) of 102 and 113
The least common multiple (LCM) of 102 and 113 is 11526.
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 113?
First, calculate the GCD of 102 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 113 = 0 remainder 102 |
| 2 | 113 ÷ 102 = 1 remainder 11 |
| 3 | 102 ÷ 11 = 9 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 51 | 9588 |
| 56 and 128 | 896 |
| 189 and 40 | 7560 |
| 199 and 111 | 22089 |
| 48 and 33 | 528 |