Least Common Multiple (LCM) of 102 and 42
The least common multiple (LCM) of 102 and 42 is 714.
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 42?
First, calculate the GCD of 102 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 42 = 2 remainder 18 |
| 2 | 42 ÷ 18 = 2 remainder 6 |
| 3 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 63 | 126 |
| 81 and 135 | 405 |
| 65 and 45 | 585 |
| 95 and 141 | 13395 |
| 37 and 65 | 2405 |