Least Common Multiple (LCM) of 102 and 168
The least common multiple (LCM) of 102 and 168 is 2856.
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 168?
First, calculate the GCD of 102 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 168 = 0 remainder 102 |
| 2 | 168 ÷ 102 = 1 remainder 66 |
| 3 | 102 ÷ 66 = 1 remainder 36 |
| 4 | 66 ÷ 36 = 1 remainder 30 |
| 5 | 36 ÷ 30 = 1 remainder 6 |
| 6 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 29 | 1856 |
| 140 and 15 | 420 |
| 161 and 61 | 9821 |
| 55 and 175 | 1925 |
| 68 and 80 | 1360 |