Least Common Multiple (LCM) of 102 and 142
The least common multiple (LCM) of 102 and 142 is 7242.
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 142?
First, calculate the GCD of 102 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 142 = 0 remainder 102 |
| 2 | 142 ÷ 102 = 1 remainder 40 |
| 3 | 102 ÷ 40 = 2 remainder 22 |
| 4 | 40 ÷ 22 = 1 remainder 18 |
| 5 | 22 ÷ 18 = 1 remainder 4 |
| 6 | 18 ÷ 4 = 4 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 123 | 22632 |
| 157 and 192 | 30144 |
| 185 and 174 | 32190 |
| 18 and 79 | 1422 |
| 14 and 139 | 1946 |