Least Common Multiple (LCM) of 42 and 198
The least common multiple (LCM) of 42 and 198 is 1386.
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 42 and 198?
First, calculate the GCD of 42 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 198 = 0 remainder 42 |
| 2 | 198 ÷ 42 = 4 remainder 30 |
| 3 | 42 ÷ 30 = 1 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 43 | 645 |
| 87 and 65 | 5655 |
| 120 and 169 | 20280 |
| 53 and 152 | 8056 |
| 103 and 112 | 11536 |