Least Common Multiple (LCM) of 42 and 99
The least common multiple (LCM) of 42 and 99 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 99?
First, calculate the GCD of 42 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 99 = 0 remainder 42 |
| 2 | 99 ÷ 42 = 2 remainder 15 |
| 3 | 42 ÷ 15 = 2 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 133 | 17822 |
| 68 and 177 | 12036 |
| 185 and 53 | 9805 |
| 80 and 78 | 3120 |
| 157 and 157 | 157 |