Least Common Multiple (LCM) of 105 and 102
The least common multiple (LCM) of 105 and 102 is 3570.
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 105 and 102?
First, calculate the GCD of 105 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 102 = 1 remainder 3 |
| 2 | 102 ÷ 3 = 34 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 169 | 6760 |
| 123 and 190 | 23370 |
| 105 and 192 | 6720 |
| 115 and 107 | 12305 |
| 160 and 196 | 7840 |